Power system multi-modal scheduling method and system based on core-storage collaborative optimization

Through the multi-modal scheduling method of nuclear-storage collaborative optimization of power system, the transmission and distribution collaborative scheduling system is decoupled, representative scenarios are generated, nuclear-storage collaborative scheduling model is constructed, and the output of nuclear power and energy storage is optimized. The problems of limited nuclear power regulation capacity and insufficient energy storage capacity are solved, and the frequency regulation and new energy consumption capacity of the power grid are improved.

CN120377379APending Publication Date: 2025-07-25NAT NUCLEAR DEMONSTRATION POWER PLANT CO LTD
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Patent Information

Application Number
CN202510455243.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-11
Publication Date
2025-07-25

AI Technical Summary

Technical Problem

The existing technology fails to fully utilize the complementary characteristics of nuclear power and energy storage, resulting in limited nuclear power regulation capabilities, inability to respond quickly to load changes, limited energy storage capacity, unable to meet the peak and frequency regulation needs of the power system, and unable to effectively absorb new energy. Especially in areas with high renewable energy permeability, nuclear power equipment utilization rate is low and wind curtailment is severe.

Method used

By building a multi-modal scheduling method for nuclear-storage collaborative optimization of power system, decoupling the transmission and distribution collaborative scheduling system, using cubic sampling and scenario reduction technologies to generate representative scenarios, construct a nuclear-storage collaborative scheduling model, perform joint scheduling, and combine frequency safety constraints to optimize the output of nuclear power units, thermal power units and energy storage devices to achieve coordinated scheduling.

Benefits of technology

It has improved the system frequency regulation capability and new energy consumption level, alleviated the peak load pressure of the power grid, reduced the system operation cost and wind and light abandonment rate, improved the utilization efficiency of renewable energy such as wind power and photovoltaics, and achieved deep participation in the power grid peak regulating and frequency regulation.

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Abstract

The invention provides an electric power system multi-modal scheduling method and system based on nuclear-storage collaborative optimization, relates to the technical field of electric power system scheduling control, and aims to solve the problems that nuclear-storage complementary characteristics are not fully utilized and various demand regulation of resources such as nuclear power and energy storage cannot be fully exerted in the prior art. Comprising the steps of analyzing a mechanism that nuclear power and energy storage cooperatively participate in peak regulation and frequency modulation; the method comprises the following steps of: decoupling a scheduling demand of a transmission and distribution cooperative scheduling system, constructing a new energy output scene by adopting cubic sampling based on the decoupled transmission and distribution cooperative scheduling system, and generating a representative scene through a scene reduction technology; and based on the representative scene, through a core-storage cooperative scheduling model, carrying out combined scheduling on the transmission and distribution cooperative scheduling system. According to the method, peak regulation and frequency modulation combined optimization under bilateral nuclear storage coordination of the power transmission network and the power distribution network is realized, the system frequency regulation capability and the new energy consumption level are improved, the peak load pressure of the power grid is effectively relieved, and the bearing capability of the power transmission network to the power distribution network is improved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of power system dispatching control, and particularly relates to a multi-modal dispatching method and system for a power system based on nuclear-storage collaborative optimization. Background Technique

[0002] The statements in this part merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] In recent years, the climate problem has become increasingly severe, pollution control is urgent, and investment in fossil fuels has continued to decline. Developing renewable energy technologies vigorously has become a consensus in the energy field. Among them, nuclear energy, as one of the cleanest and most efficient low-carbon energy sources and forms, has a full-life-cycle carbon emission of only about 12 g / kWh, has characteristics such as a large installed capacity, stable and reliable operation, and a long refueling cycle, and has strong frequency and voltage support capabilities. Therefore, the vigorous development of nuclear energy can not only provide sufficient power guarantee, play an important role in promoting energy transformation and global development, but also play an important role in addressing global climate change and ensuring energy security.

[0004] A large number of scholars have widely carried out research on nuclear power participating in frequency regulation around the safety goal. A method of combining nuclear power units with a hydrogen energy complex to participate in the primary frequency regulation of the power system is proposed. Hydrogen and oxygen are generated by electrolyzing water, and energy is accumulated by accumulating hot water in a tank. The accumulated energy is used to generate electricity to complete the first frequency regulation command; taking a nuclear power plant in Fujian Province as the research object, research is carried out on aspects such as the proportion of nuclear power installed capacity, frequency change, and frequency regulation dead zone, providing a theoretical basis for nuclear power units to participate in the primary frequency regulation of the power grid; the feasibility of nuclear power units participating in the primary frequency regulation of the power grid is studied, a primary frequency regulation model of nuclear power units is established, and the R-rod control method is adopted. The simulation results show that nuclear power units can participate in the primary frequency regulation of the power grid; using the mechanism modeling method, a model of a nuclear power unit's steam turbine participating in the primary frequency regulation is established, and a steam turbine power-frequency control system is constructed. The simulation results achieve the initial tracking of the power grid load.

[0005] With the construction of clean energy projects in coastal areas and the increasing load volatility, the peak shaving and frequency regulation pressures of the power system are increasing day by day, and the demand for the dispatching ability of nuclear power is increasing. However, the output regulation ability of nuclear power is limited and it cannot quickly respond to load changes; while the energy storage system has a fast response ability but limited capacity. Nuclear power and energy storage systems have their own advantages in terms of time and space distribution. However, how to accurately evaluate their spatio-temporal complementarity and evaluate the synergistic effects under different peak shaving and frequency regulation scenarios is the key difficulty in constructing a collaborative mechanism.

[0006] At the same time, existing research cannot meet the goal of balancing security and full consumption of new energy. In particular, the output of wind power is random and has the characteristics of reverse peak regulation, resulting in serious curtailment of wind power. Moreover, in the current operation of the power system, nuclear power units are often required to operate with base load, which puts high requirements on the flexible operation of other power sources in the system. Even in system dispatching, some nuclear power units are required to reduce power or even shut down, severely restricting the utilization rate of nuclear power equipment, especially in areas with a high penetration rate of renewable energy such as nuclear power. Summary of the Invention

[0007] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a multi-modal dispatching method and system for a power system based on nuclear-storage collaborative optimization, analyzes the spatio-temporal complementary characteristics of nuclear power units and energy storage devices, fully explores the collaborative effect of the two in peak shaving and frequency modulation, and establishes a dispatching model for nuclear-storage collaboration; and constructs a collaborative dispatching framework for transmission and distribution, decouples the dispatching requirements of the transmission network and the distribution network, and formulates a reasonable day-ahead optimization strategy; introduces frequency security constraints, thereby reducing the total system cost, improving the new energy consumption level and enhancing the frequency regulation ability.

[0008] To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:

[0009] The first aspect of the present invention provides a multi-modal dispatching method for a power system based on nuclear-storage collaborative optimization, including:

[0010] Decouple the dispatching requirements of the collaborative dispatching system for transmission and distribution to obtain the decoupled collaborative dispatching system for transmission and distribution;

[0011] Based on the decoupled collaborative dispatching system for transmission and distribution, construct new energy output scenarios by using cubic sampling, and generate representative scenarios through scenario reduction technology;

[0012] Based on the decoupled collaborative dispatching system for transmission and distribution and the representative scenarios, construct a nuclear-storage collaborative dispatching model;

[0013] Based on the nuclear-storage collaborative dispatching model, perform joint dispatching on the collaborative dispatching system for transmission and distribution;

[0014] Among them, construct the objective function of the nuclear-storage collaborative dispatching model, solve the objective function of the nuclear-storage collaborative dispatching model to obtain the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units;

[0015] Based on the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units, perform joint dispatching on the collaborative dispatching system for transmission and distribution.

[0016] As an implementation, based on the nuclear-storage collaborative dispatching model, perform joint frequency modulation on the collaborative dispatching system for transmission and distribution. The specific process is as follows:

[0017] Calculate the difference between the grid frequency and the rated frequency to obtain the frequency deviation;

[0018] Determine whether the frequency deviation is within the primary frequency regulation dead zone. If it is, neither the energy storage device nor the nuclear power unit responds. If not, determine whether the frequency deviation is within the small disturbance interval. If it is, the energy storage device quickly responds to the frequency regulation command. If not, the energy storage device and the nuclear power unit perform combined abnormal frequency regulation.

[0019] As an implementation, in the framework of the transmission and distribution coordinated dispatching system, decouple the exchange power of the boundary tie lines of the transmission and distribution coordinated dispatching system.

[0020] As an implementation, construct new energy output scenarios based on Latin hypercube sampling, and generate representative scenarios through scenario reduction technology. The specific process is as follows:

[0021] Obtain multiple wind power output scenarios through Latin hypercube sampling;

[0022] Adopt a scenario reduction model with Kantorovich distance to reduce multiple wind power output scenarios to obtain representative scenarios.

[0023] As an implementation, adopt a scenario reduction model with Kantorovich distance to reduce multiple wind power output scenarios. The specific process is as follows:

[0024] Calculate the Kantorovich distance of different wind power output scenarios;

[0025] Select any scenario, calculate the distance between each scenario and the selected scenario, multiply it by the probability of the selected scenario, delete the scenario with the closest distance to the selected scenario according to the product size, and update the probability of the set scenario;

[0026] Repeat the above steps until the scenarios are reduced to the preset number.

[0027] As an implementation, the constraint conditions include transmission network constraints and distribution network constraints;

[0028] Among them, the transmission network constraints include power balance constraints, thermal power unit constraints, nuclear power unit constraints, frequency safety constraints, branch power flow constraints, and transmission and distribution network tie line exchange power transmission constraints;

[0029] The distribution network constraints include power balance constraints, thermal power unit constraints, energy storage state of charge constraints, distribution network power flow constraints, transmission and distribution network tie line exchange power transmission constraints, and comprehensive norm constraints.

[0030] As an implementation, the objective function of the nuclear-storage coordinated dispatching model is optimized with the minimum total cost of the transmission and distribution network. The formula is:

[0031]

[0032] Where: C TA is the operating cost of the transmission grid; k is the number of distribution grids; C DA,k is the operating cost of the k-th distribution grid; N n represents the number of representative scenarios.

[0033] The second aspect of the present invention provides a multi-modal power system scheduling system based on nuclear-storage collaborative optimization, including:

[0034] A decoupling module for the transmission and distribution collaborative scheduling system, which is used to decouple the scheduling requirements of the transmission and distribution collaborative scheduling system to obtain the decoupled transmission and distribution collaborative scheduling system;

[0035] A wind power output scenario generation module, which is used to construct new energy output scenarios by cubic sampling based on the decoupled transmission and distribution collaborative scheduling system, and generate representative scenarios through scenario reduction technology;

[0036] A joint scheduling module for the nuclear-storage collaborative scheduling model, which is used to construct a nuclear-storage collaborative scheduling model based on the decoupled transmission and distribution collaborative scheduling system and representative scenarios;

[0037] Based on the nuclear-storage collaborative scheduling model, perform joint scheduling on the transmission and distribution collaborative scheduling system;

[0038] Among them, construct the objective function of the nuclear-storage collaborative scheduling model, solve the objective function of the nuclear-storage collaborative scheduling model, and obtain the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units;

[0039] Based on the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units, perform joint scheduling on the transmission and distribution collaborative scheduling system.

[0040] The third aspect of the present invention provides a computer device, including a memory, a processor, and a program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps in the method described in the first aspect of the present invention.

[0041] The fourth aspect of the present invention aims to provide a computer-readable storage medium, on which a program is stored, and when the program is executed by a processor, it implements the steps in the method described in the first aspect of the present invention.

[0042] The above one or more technical solutions have the following beneficial effects:

[0043] This embodiment solves the problem of improving the dispatching of new - energy carrying capacity with nuclear - storage coordination under peak - shaving and frequency - modulation constraints, analyzes the mechanism of nuclear power and energy storage participating in peak - shaving and frequency - modulation synergistically, and constructs new - energy output scenarios under comprehensive norm constraints based on the framework of coordinated transmission and distribution dispatching. Through detailed case studies, the effectiveness and practical performance of the proposed method in improving the system's frequency regulation ability and new - energy consumption level are verified.

[0044] In this embodiment, by decoupling the dispatching requirements between the transmission grid and the distribution grid and formulating a reasonable day - ahead optimization strategy, the carrying capacity of the transmission grid for the distribution grid is improved. Combining the self - stability and self - regulation characteristics of nuclear power with the fast - response ability of energy storage, the peak - shaving and frequency - modulation control of nuclear - storage coordination is realized, effectively alleviating the peak - load pressure of the power grid, reducing the system operation cost and the curtailment rate of wind and light, and improving the utilization efficiency of renewable energy such as wind power and photovoltaic power.

[0045] In this embodiment, by introducing frequency - safety constraints, the synergistic effect of nuclear power and energy storage in frequency regulation is deeply explored. By tapping the regulation potential of nuclear power and energy storage and relaxing the frequency - safety constraints, the system can still maintain frequency stability when the frequency - regulation ability is insufficient, thus significantly improving the new - energy consumption capacity.

[0046] The method for improving the dispatching of new - energy carrying capacity with nuclear - storage coordination under peak - shaving and frequency - modulation constraints proposed in this embodiment provides new ideas and theoretical support for nuclear power units to deeply participate in the peak - shaving and frequency - modulation of the power grid, has important significance for realizing the safe and stable operation of the power system under high - proportion new - energy access, and provides a reference basis for the operation of the power system under high - proportion new - energy access in the future.

[0047] Advantages of additional aspects of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The schematic diagrams in the specification forming a part of the present invention are used to provide a further understanding of the present invention. The illustrative embodiments and descriptions thereof are used to explain the present invention and do not constitute an improper limitation of the present invention.

[0049] Figure 1 It is a flowchart of a multi - modal dispatching method for a power system based on nuclear - storage collaborative optimization according to Embodiment 1 of the present invention;

[0050] Figure 2 It is a schematic diagram of the principle of the self - regulation characteristic of the power of a nuclear power unit according to Embodiment 1 of the present invention;

[0051] Figure 3 It is the peak - shaving principle of a nuclear power unit according to Embodiment 1 of the present invention;

[0052] Figure 4 Output of the energy storage participating in peak shaving and frequency modulation coordination scenario in the first embodiment of the present invention;

[0053] Figure 5 Division of the collaborative control working area based on load forecasting in the first embodiment of the present invention;

[0054] Figure 6 Flow chart of the nuclear-storage collaborative response to frequency modulation commands in the first embodiment of the present invention;

[0055] Figure 7 Transmission and distribution collaborative scheduling framework in the first embodiment of the present invention;

[0056] Figure 8 Flow chart of Latin hypercube sampling in the first embodiment of the present invention. Detailed implementation manners

[0057] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0058] It should be noted that the terms used herein are only for describing the specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention.

[0059] In the case of no conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0060] Term explanation:

[0061] Nuclear-storage coordination: Nuclear power units generally operate with base load, while energy storage has a flexible regulation function. Nuclear power units and energy storage have the potential for coordinated operation on the time scale and can effectively complement each other to participate in peak shaving and frequency modulation response of the power grid.

[0062] Transmission and distribution coordination: Coordinate the operation and optimal dispatching methods of the transmission grid and the distribution grid in the power system to improve power transmission efficiency, improve power quality, reduce losses, and enhance the adaptability to new energy and load fluctuations.

[0063] State of charge: The percentage of the current stored electricity in the battery relative to its total capacity, used to represent the proportion of the remaining available electricity in the battery.

[0064] Primary frequency modulation: An automatic regulation function in the power system where generating units automatically adjust the power generation when detecting frequency deviation and quickly respond to maintain the stability of the power grid frequency.

[0065] Secondary frequency regulation: After primary frequency regulation in the power system, further power adjustment is performed on the generator units through automatic generation control or dispatching instructions to restore the system frequency to the set value and optimize the power distribution, ensuring the frequency stability and optimal operation of the system.

[0066] Peak shaving: The regulation process of adjusting the output of generator units or starting and stopping flexible resources during peak and trough loads to smooth out load fluctuations and maintain the stable operation of the power system.

[0067] Embodiment 1

[0068] This embodiment discloses a multimodal scheduling method for a power system based on nuclear-storage collaborative optimization.

[0069] To more clearly elaborate this embodiment, the implementation process of multimodal scheduling for a power system based on nuclear-storage collaborative optimization can be specifically described as follows:

[0070] The multimodal scheduling method for a power system based on nuclear-storage collaborative optimization includes:

[0071] S1. Decouple the scheduling requirements of the transmission and distribution collaborative scheduling system to obtain the decoupled transmission and distribution collaborative scheduling system;

[0072] S2. Based on the decoupled transmission and distribution collaborative scheduling system, construct new energy output scenarios using Latin hypercube sampling, and obtain representative scenarios through scenario reduction technology;

[0073] S3. Based on the decoupled transmission and distribution collaborative scheduling system and the representative scenario probabilities, construct a nuclear-storage collaborative scheduling model;

[0074] Based on the nuclear-storage collaborative scheduling model, perform joint scheduling on the transmission and distribution collaborative scheduling system;

[0075] Among them, construct the objective function of the nuclear-storage collaborative scheduling model, solve the objective function of the nuclear-storage collaborative scheduling model to obtain the output of nuclear power units, thermal power units, energy storage devices, and the peak shaving depth of nuclear power units;

[0076] Based on the output of nuclear power units, thermal power units, energy storage devices, and the peak shaving depth of nuclear power units, perform joint scheduling on the transmission and distribution collaborative scheduling system.

[0077] Before step S1, S0. Obtain relevant data and evaluate the spatio-temporal complementary characteristics of nuclear power units and energy storage devices.

[0078] S0-1. Obtain nuclear power unit data, thermal power unit data, wind power data, and transmission and distribution grid data.

[0079] In this embodiment, the relevant parameters of thermal power units and line parameters in the transmission grid, as well as the line parameters of the distribution grid, all adopt existing data. The main data obtained for nuclear power units are shown in Table 1. Modeling is carried out using yalmip based on MATLAB, and the GUROBI solver is called for solution.

[0080] Table 1 Nuclear Power Unit Data

[0081]

[0082] Through the above steps, a multi-modal scheduling method considering the coordinated optimization of nuclear power and energy storage is constructed, providing effective support for reducing the peak shaving depth of nuclear power and improving the new energy consumption rate.

[0083] S0-2. Evaluate the spatio-temporal complementary characteristics of nuclear power units and energy storage devices, and analyze the frequency regulation ability and peak shaving ability of nuclear power.

[0084] S0-2-1. Analysis of the frequency regulation ability of nuclear power.

[0085] In this embodiment, the basic principle of nuclear power units participating in primary frequency regulation is similar to that of thermal power units. During primary frequency regulation, the change in unit power is as follows:

[0086]

[0087] where: Δf is the deviation between the rated frequency and the actual frequency; K is the regulation coefficient; f n is the rated frequency; P is the rated power.

[0088] During normal power operation, the deviation between the target speed and the actual speed of the steam turbine is regarded as the deviation of the grid frequency. The governor usually consists of a sensor, a controller, and an actuator. When the grid frequency deviates, the sensor monitors this change, the controller calculates the corresponding adjustment strategy, and the actuator adjusts the speed to ensure the synchronous operation of the generator and the grid. Through continuous feedback control, the governor adapts to the change of the grid frequency and maintains the stability of the grid.

[0089] Primary frequency regulation is mainly used to suppress large fluctuations in grid frequency, but it has limited effect on disturbances with short periods and small amplitudes, and it cannot achieve zero-error regulation. Secondary frequency regulation has an integral effect, and the regulation result has almost no static deviation, and can restore the grid frequency to the rated value. However, secondary frequency regulation usually relies on thermal power units, and nuclear power units generally do not perform secondary frequency regulation alone.

[0090] The tertiary frequency regulation of the power system is also known as the benefit allocation of active power. Its process includes: making short-term or ultra-short-term predictions of the power system load, selecting suitable units for frequency regulation according to the prediction results, and distributing the load components with the largest fluctuation amplitude and the longest change period to each generating unit according to certain principles.

[0091] As Figure 2 shown, the new generation of pressurized water reactor nuclear power units has self-stability and self-regulation. In the case where the reactor regulation system does not function, when the external load fluctuates within a certain range, it can well ensure that the active power output of the unit follows the change of the load.

[0092] S0-2-2, Analysis of nuclear power peak shaving capacity.

[0093] In this embodiment, according to the actual situation of the power grid, the nuclear power unit can flexibly participate in the system dispatching operation by changing the peak shaving depth, low-power operation time and regulation rate. The power stages and states of the nuclear power unit at the nth peak shaving depth are as Figure 3 shown.

[0094] To meet the flexibility requirements of the nuclear power unit to participate in peak shaving as much as possible, the peak shaving depth of the nuclear power unit is evenly divided into sN gears, then the nth peak shaving depth can be expressed as:

[0095]

[0096] where is the maximum output of nuclear power unit i; is the minimum output of nuclear power unit i.

[0097] The corresponding power of the low-power stage of the nuclear power can be expressed as:

[0098]

[0099] The linear change time of the nuclear power unit power is generally 1-3h, so three power transition states are set at each gear: two states d n,1 and d n,3 are set when the linear change time is 3h; one state d n,2 is set when the linear change time is 2h; no power state is set when the linear change time is 1h. According to the state division, the corresponding nuclear power can be expressed as:

[0100]

[0101] where j is the transition state label when the power rises or falls, and j = 1, 2, 3.

[0102] Then the power of nuclear power unit i in the first time period can be expressed as:

[0103]

[0104] Among them, q t is the full-power operation flag; l n,t is the low-power operation flag at time t under the peaking depth of the nth gear; d n,j,t is the power increase and decrease operation flag at the peaking depth of the nth gear, the jth state, and the tth time period.

[0105] To ensure that the nuclear power unit operates at only one power, the following constraints should also be satisfied:

[0106]

[0107] When the nuclear power unit operates in the full-low power state, it needs to operate stably for a certain period of time continuously. The constraints to be satisfied are:

[0108]

[0109] Among them, T h N and T l N are the minimum continuous operation times for full power and low power respectively.

[0110] When increasing or decreasing the power, the operation flag also needs to satisfy the time coupling constraint. The operation flag coupling constraint when the power increase and decrease time is 2h is:

[0111]

[0112] The operation flag coupling constraint when the power increase and decrease time is 3h is:

[0113]

[0114] S0-2-3. There are complementary characteristics of peaking and frequency modulation between nuclear power and energy storage.

[0115] The power system responds to the peaking demand mainly relying on cold reserve, and responds to the frequency modulation demand mostly relying on hot reserve. There are complementary characteristics of peaking and frequency modulation between nuclear power and energy storage. The following analyzes the control methods and constraints for nuclear energy storage to participate in peaking and frequency modulation synergistically.

[0116] Limited by the energy storage capacity, when energy storage is applied to the coordinated control of peak shaving and frequency regulation, the impact of the state of charge (SOC) must be considered. When operating in the valley filling area, the energy storage is in the charging state, and its SOC rises from 0.1 to 0.9. When operating in the peak shaving area, the energy storage is in the discharging state, and the SOC drops from 0.9 to 0.1. At this time, when the ES switches to the frequency regulation area, the initial value of the SOC may be 0.1 or 0.9. However, the frequency deviation has two-way possibilities. Therefore, when the SOC is 0.1, the problem of frequency drop cannot be improved by discharging, and when the SOC is 0.9, the problem of frequency rise cannot be improved by charging. To avoid having the SOC at the critical value and reducing the frequency regulation ability. In this paper, the SOC peak shaving working range is set to 0.15 - 0.85.

[0117] The process of energy storage participating in the coordinated scenario of peak shaving and frequency regulation is shown as Figure 3 follows. Figure 3 In dead , Δf g is the frequency deviation dead zone value, taking 0.033 Hz; P f (t) and P bess (t) are the planned valley filling line and the planned peak shaving line at time t respectively; P PFR (t) is the charge and discharge amount of the ES; P

[0118] ΔP PFR_i = K i ×Δf (10)

[0119] K i = P N / f N (11)

[0120] Among them, ΔP PFR_i is the frequency regulation output power of the i-th unit; Δf is the frequency deviation; K i is the unit power regulation coefficient; P N , f N are the rated power and rated frequency of the energy storage respectively.

[0121] Through the above steps, the physical process of energy storage participating in peak shaving and frequency regulation is accurately described, and the complementary characteristics of nuclear power and energy storage can be accurately evaluated, providing a prerequisite for realizing the multimodal scheduling of the power system based on nuclear-storage collaborative optimization.

[0122] As Figure 1 shown, in step S1, the scheduling requirements of the transmission and distribution collaborative scheduling system are decoupled to obtain the decoupled transmission and distribution collaborative scheduling system.

[0123] AsFigure 7 As shown in the figure, in this embodiment, to meet the scheduling requirements of various types of autonomous entities, a transmission and distribution collaborative scheduling system framework is constructed. The transmission and distribution collaborative scheduling system framework includes a transmission network layer and a distribution network layer. Among them, the transmission network layer includes traditional generating units, new energy generation, loads, and the transmission network. The distribution network layer includes several active distribution networks, controllable distributed power sources, distributed renewable power sources, energy storage, and loads.

[0124] Among them, P1 trans , P2 trans , P n trans are the active powers transmitted from the transmission network to the 1st, 2nd, …, nth distribution networks respectively; P1 dist , P2 dist , P n dist are the transmission powers purchased by the 1st, 2nd, …, nth distribution networks from the transmission network respectively.

[0125] The stakeholders of the transmission network and the distribution network are different, and their scheduling objectives are also different. When conducting scheduling, the strong coupling of the operation of the transmission and distribution systems must be considered. To achieve the purpose of centralized optimization of transmission and distribution collaboration and avoid problems such as communication overload and data loss caused by a large amount of data transmission, the exchanged power of the boundary tie lines of the transmission and distribution collaborative system is decoupled, and the formula is:

[0126]

[0127] Among them, is the active power transmitted from the transmission network to the kth distribution network at time t; is the transmission power purchased by the kth distribution network from the transmission network at time t.

[0128] Through the above steps, the problems of huge calculation amount and complex calculation caused by coupling in the optimization calculation process of the transmission network and the distribution network are solved.

[0129] As Figure 1 shown, in step S2, based on the decoupled transmission and distribution collaborative scheduling system, cubic sampling is used to construct new energy output scenarios, and representative scenarios are generated through scenario reduction technology.

[0130] In the traditional sense, exact probabilities use a certain explicit probability to describe the possibility of a specific random event occurring. However, when the number of observed samples is limited, the statistical information they contain may not be sufficient to fully describe the actual statistical laws. Therefore, it is difficult to ensure the authenticity of the results and their credibility is not high to estimate exact probabilities from limited samples.

[0131] In this embodiment, based on a limited wind power data set, feasible wind power output scenarios and their probabilities are generated through scenario generation and reduction, and a comprehensive norm constraint is constructed in the following text to fully consider the uncertainty of wind power.

[0132] Based on Latin hypercube sampling, new energy output scenarios are constructed, and representative scenarios are generated through scenario reduction technology. The specific process is as follows:

[0133] (1) Multiple wind power output scenarios are obtained through Latin hypercube sampling.

[0134] Latin hypercube sampling is a multidimensional uniform stratified sampling method that has high-precision results at a smaller sampling scale. Based on this, this paper uses Latin hypercube sampling to establish random scenarios for wind power output, such as Figure 8 is the Latin hypercube sampling process.

[0135] (2) The scenario reduction model of Kantorovich distance is used to reduce multiple wind power output scenarios to obtain representative scenarios.

[0136] The N wind power output scenarios obtained through Latin hypercube sampling have a high correlation, which not only has a large amount of data but also has low practicality. Therefore, the scenario reduction model of Kantorovich distance is used to reduce N scenarios to more representative n scenarios. The specific process is as follows:

[0137] 1) Calculate the Kantorovich distance for different scenes.

[0138] Calculate the Kantorovich distance D of scenes si and sj k (si,sj).

[0139] 2) Select any scene, calculate the distance between each scene and the selected scene, and multiply it with the probability of the selected scene. According to the size of the product, delete the scene closest to the selected scene and update the probability of the set scene.

[0140] Select any setting scene r , calculate each scene and scene s r The distance and its product with the scene probability PD r , select the scene closest to sr, delete it, and update scene s r probability.

[0141] 3) Repeat the above steps until the number of scenes is reduced to the preset number.

[0142] After the above steps, the uncertainty of new energy output is effectively characterized through several representative scenarios.

[0143] likeFigure 1 As shown, in step S3, based on the decoupled transmission and distribution coordinated scheduling system and representative scenarios, a nuclear-storage coordinated scheduling model is constructed.

[0144] Based on the nuclear-storage coordinated scheduling model, joint scheduling is performed on the transmission and distribution coordinated scheduling system.

[0145] S3-1. Based on the decoupled transmission and distribution coordinated scheduling system and representative scenarios, a nuclear-storage coordinated scheduling model is constructed.

[0146] The nuclear-storage coordinated scheduling model includes an objective function and constraint conditions.

[0147] In this embodiment, with the minimum total cost of the transmission and distribution network as the objective function, mainly consider minimizing the total cost C of the transmission and distribution network.

[0148]

[0149] Among them, C TA is the operating cost of the transmission network; k is the number of distribution networks; C DA,k is the operating cost of the kth distribution network.

[0150] (1) Transmission network cost

[0151] The optimization objective of the transmission network layer is to coordinate the output of nuclear power plants, thermal power plants and wind power to improve the efficiency of the transmission network. Therefore, the transmission network cost formula is:

[0152] C TA = C TG + C GU + C w + C N - C sell (14)

[0153] Among them, C TG 、C GU 、C W 、C N 、C sell are the fuel cost of thermal power plants, the start-stop cost of thermal power plants, the penalty cost of wind power curtailment in the transmission network, the operating cost of nuclear power, and the power sales revenue of the transmission network, respectively.

[0154] (2) Distribution network cost

[0155] The optimization objective of the distribution network layer is to absorb more wind power through energy storage regulation, reduce the cost of purchasing electricity from the transmission network, and thus improve the economy of the distribution network. Taking the kth distribution network as an example, its cost is expressed as follows:

[0156] C DA,k = C CDG,k + C RDG,k + C buy,k+C ESS,k (15)

[0157] Among them, C CDG,k , C RDG,k , C buy,k , C ESS,k are respectively the controllable distributed energy generation cost, the distributed renewable energy curtailment cost, the cost of purchasing electricity from the transmission grid, and the energy storage device cost of the k-th distribution network.

[0158] In this embodiment, the objective function needs to satisfy specific constraint conditions. The constraint conditions include transmission grid constraints and distribution network constraints.

[0159] Among them, the obtained nuclear power unit data, thermal power unit data, wind power data, and transmission and distribution network data form specific constraint conditions.

[0160] Among them, the transmission grid constraints include power balance constraints, thermal power unit constraints, nuclear power unit constraints, frequency safety constraints, branch power flow constraints, and transmission and distribution network tie-line exchange power transmission constraints.

[0161] The distribution network constraints include power balance constraints, thermal power unit constraints, energy storage state of charge constraints, distribution network power flow constraints, transmission and distribution network tie-line exchange power transmission constraints, and comprehensive norm constraints.

[0162] (1) Transmission grid constraints

[0163] The transmission grid layer constraint conditions include thermal power unit start-stop constraints, output constraints, ramp constraints, as well as wind farm output constraints, transmission and distribution network tie-line exchange power transmission constraints, power balance constraints, and line power flow constraints.

[0164] 1) Power balance constraints

[0165]

[0166] Among them, are respectively the thermal power units and wind turbine sets on node d; Ω D v is the total transmission grid load; Ω p is the set of distribution networks on node d.

[0167] 2) Thermal power unit constraints

[0168] The thermal power unit constraints include unit output constraints and unit ramp constraints:

[0169]

[0170] -P down ,i ≤P i,t -Pi,t-1 ≤P up,i (18)

[0171] wherein, are respectively the maximum output and minimum output of thermal power unit i in the t-th period; are respectively the primary frequency regulation upward and downward reserve of thermal power unit i in the t-th period; are respectively the secondary frequency regulation upward and downward reserve of thermal power unit i in the t-th period.

[0172] 3) Nuclear power unit constraints

[0173] In this paper, a fixed gear operation mode of the nuclear power unit is selected, and a continuous variable is introduced Set the peak shaving depth of the unit to be The nuclear power output expression is:

[0174]

[0175] wherein, y is the unit transition state flag variable; are respectively the maximum and minimum output powers of the nuclear power unit; and represent the increase / decrease power of different state labels of the nuclear power unit at the peak shaving depth of .

[0176] In addition, the nuclear power unit constraints also include (5) to (9) derived above.

[0177] 4) Frequency safety constraints

[0178] The frequency safety constraints include quasi-steady state frequency constraints and dynamic frequency constraints.

[0179] The quasi-steady state frequency safety constraints can be derived from the swing equation. At this time, the frequency change rate can be set to 0:

[0180]

[0181] wherein, Δf ss is the maximum allowable frequency deviation in the quasi-steady state; P d is the total load; ΔP L is the total change in load power; D is the load damping coefficient.

[0182] Meanwhile, a constraint is established to limit the frequency deviation during the power change process. The formula is:

[0183] -Δf max ≤Δf t dn ≤0≤Δf t up ≤Δf max(21)

[0184]

[0185] Among them, Δf max is the maximum allowable frequency deviation; Δf t dn , Δf t up are respectively the boundaries of the decision values of the deviation from the rated frequency in time period t; R g is the frequency modulation coefficient of unit g; ΔP i,t up , ΔP i,t dn are the power fluctuations above and below the system power.

[0186] 5) Branch power flow constraint

[0187]

[0188] Among them, δ d,l is the power transfer distribution factor of node d to line l; K l is the upper limit of the power flowing through line l; P d,t is the active power of node d.

[0189] 6) Transmission constraint of the interchange power of the transmission and distribution network tie line

[0190]

[0191] Among them, D is the load set; P k,t T→D is the interchange power of the tie line between the transmission network TG and the ADN; P k T→D,max , P k T→D,min are respectively the upper and lower limits of the transmission power of the tie line between TG and ADN.

[0192] (2) Distribution network constraint

[0193] The constraint conditions at the distribution network layer mainly include node power balance constraint, energy storage charge and discharge power constraint, energy storage charge and discharge state constraint, transmission and distribution network tie line interchange power transmission constraint, line capacity constraint, energy storage state of charge constraint, distribution network power flow constraint, etc.

[0194] 1) Power balance constraint

[0195]

[0196] Among them, Ω d NG , Ω d NwThey are the sets of thermal power units and wind power units on node d respectively; Ωp is the total load of the transmission grid; Ωd * is the set of distribution grids on node d.

[0197] 2) Constraints of thermal power units

[0198] Same as the constraints of thermal power units in the transmission grid.

[0199] 3) Constraints on the state of charge of energy storage

[0200]

[0201] Among them, σ is the self-loss rate of the energy storage device; η k c and η k d are the charging and discharging efficiencies of the energy storage device in the kth distribution grid respectively; is the capacity of the mth energy storage device in the kth distribution grid.

[0202] 4) Constraints on distribution grid power flow

[0203]

[0204] Among them, u(f) is the set of end nodes of the branch with f as the initial node; V e,t and V f,t are the voltages of nodes e and f at time t respectively; P ef,t , Q ef,t are the active and reactive powers flowing from node e to node f at time t respectively; r ef and x ef are the reactance and resistance between branches e and f respectively; P fj,t , Q fj,t are the active and reactive powers flowing from node f to node i at time t respectively; Δt is the time interval, taking 1 h.

[0205] 5) Constraints on the exchange power transmission of the transmission-distribution network tie line

[0206] Same as the constraints on the exchange power transmission of the transmission-distribution network tie line in the transmission grid.

[0207] 6) Comprehensive norm constraints

[0208] For a given set of historical wind power output data, it is easy to construct a histogram to fit all the data. When the data scale approaches infinity, the reference distribution of wind power will converge to the true distribution under the 1-norm and ∞-norm. Therefore, the above two norms are used to construct two confidence sets. That is, using these two norm constraints can ensure the convergence of the model. Define the two confidence sets as Ω1 and Ω∞ respectively, and the formula is:

[0209]

[0210] where: p k 0 is the initial probability of the k-th scenario obtained from the historical wind power data; θ1 and θ ∞ are tolerance values determined by the given confidence level and the amount of historical data; Equations (31) are the 1-norm and ∞-norm constraint conditions respectively.

[0211] After the above steps, the wind power uncertainty is bounded by the comprehensive norm constraint, and an uncertainty set of scenario probabilities is constructed.

[0212] S3-2. Jointly dispatch the transmission and distribution coordinated dispatch system based on the nuclear-storage coordinated dispatch model.

[0213] S3-2-1. Solve the objective function of the nuclear-storage coordinated dispatch model based on the constraint conditions to obtain the output powers of the nuclear power unit, thermal power unit, energy storage device, and the peak shaving depth of the nuclear power unit;

[0214] Solve the objective function of the model and perform model linearization.

[0215] (1) Linearization of the comprehensive norm constraint

[0216] Constraint (31) is an absolute value constraint, which is not convenient for the solver to solve. In this paper, binary variables and are introduced to process it into a linear constraint as follows:

[0217]

[0218] where, and are the positive and negative deviations of p k relative to respectively. The 1-norm constraint in Equation (34) is transformed into:

[0219]

[0220] The processing method for Ω∞ is the same as the above method. Binary variables y k + and y k - are introduced:

[0221]

[0222] The ∞-norm constraint in Equation (33) is transformed into:

[0223]

[0224] (2) Piecewise linearization of the unit cost function

[0225] The operating cost of a thermal power unit is a quadratic function of the unit output power, making the objective function of the model a non-linear function. When the number of units or the scheduling period in the model increases, the time cost and difficulty of solving this optimization problem will increase significantly. Based on this, in order to reduce the difficulty of model solving and accelerate the optimization solving calculation speed, the piecewise linearization method is used to convert the unit cost function into a linear function, and then the entire optimization model is transformed into a linear programming model. The cost function image of the unit is as Figure 8 shown, where the red line segment represents the linearized cost function of the thermal power unit, and the black curve represents the operating cost function of the thermal power unit before linearization.

[0226]

[0227]

[0228] Among them, are the continuous variable and the 0-1 variable of each segment respectively, and d l G 、f l G are the abscissa and ordinate of the segmentation point respectively, and m is the number of segments.

[0229] Based on the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units, joint scheduling is carried out for the transmission and distribution coordinated scheduling system.

[0230] As Figure 5 shown, in this embodiment, joint frequency modulation is carried out for the transmission and distribution coordinated scheduling system, and the specific process is as follows:

[0231] (1) Obtain the grid frequency and calculate the difference between it and the rated frequency to obtain the frequency deviation.

[0232] (2) Determine whether the frequency deviation is within the primary frequency modulation dead zone. If it is, neither the energy storage device nor the nuclear power unit responds; if not, determine whether the frequency deviation is within the small disturbance interval. If it is, the energy storage device quickly responds to the frequency modulation command. If not, the energy storage device and the nuclear power unit perform joint abnormal frequency modulation adjustment.

[0233] In the combined primary frequency regulation system of a nuclear power unit and an energy storage array, when the frequency of the power grid fluctuates within a small range after exceeding the dead zone, the energy storage can utilize its advantage of rapid response in primary frequency regulation to quickly suppress the deterioration of frequency and maintain the stability of the power grid frequency. In this condition, only the energy storage participates in the primary frequency regulation control, and there is no need for the nuclear power unit to participate. When the power grid frequency fluctuates significantly, the energy storage and the nuclear power unit are used to jointly regulate the large disturbance section through primary frequency regulation, that is, the nuclear power unit starts to generate power, and the energy storage array compensates for the difference, so that an efficient primary frequency regulation cooperation can be formed between the energy storage array and the nuclear power unit.

[0234] Embodiment 2

[0235] The purpose of this embodiment is to provide a multimodal scheduling system for a power system based on nuclear-storage collaborative optimization, including:

[0236] A decoupling module for the transmission and distribution collaborative scheduling system, which is used to decouple the scheduling requirements of the transmission and distribution collaborative scheduling system to obtain the decoupled transmission and distribution collaborative scheduling system;

[0237] A wind power output scenario generation module, which is used to construct new energy output scenarios based on the decoupled transmission and distribution collaborative scheduling system by using cubic sampling, and generate representative scenarios through scenario reduction technology;

[0238] A joint scheduling module for the nuclear-storage collaborative scheduling model, which is used to construct a nuclear-storage collaborative scheduling model based on the decoupled transmission and distribution collaborative scheduling system and the representative scenarios;

[0239] Based on the nuclear-storage collaborative scheduling model, jointly schedule the transmission and distribution collaborative scheduling system;

[0240] Among them, the objective function of the nuclear-storage collaborative scheduling model is constructed, and the objective function of the nuclear-storage collaborative scheduling model is solved to obtain the power outputs of the nuclear power unit, the thermal power unit, the energy storage device, and the peak shaving depth of the nuclear power unit;

[0241] Based on the power outputs of the nuclear power unit, the thermal power unit, the energy storage device, and the peak shaving depth of the nuclear power unit, jointly schedule the transmission and distribution collaborative scheduling system.

[0242] Based on the provided multimodal scheduling system for a power system based on nuclear-storage collaborative optimization, the method steps in Embodiment 1 are realized.

[0243] Embodiment 3

[0244] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the above method are realized.

[0245] Embodiment 4

[0246] The purpose of this embodiment is to provide a computer-readable storage medium.

[0247] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it executes the steps of the above method.

[0248] Embodiment Five

[0249] The purpose of this embodiment is to provide a computer program product containing instructions, which, when running on a computer, enables the computer to execute the methods and functions involved in any one of the above embodiments.

[0250] Each step involved in the device of the above embodiments corresponds to the first method embodiment, and the specific implementation manner can refer to the relevant description part of the first embodiment. The term "computer-readable storage medium" should be understood to include a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0251] Those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be separately made into individual integrated circuit modules, or multiple modules or steps among them can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0252] Although the specific implementation manner of the present invention has been described above in conjunction with the drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

Claims

1. A multimodal scheduling method for a power system based on nuclear-storage collaborative optimization, characterized in that, Including: Decouple the scheduling requirements of the transmission and distribution collaborative scheduling system to obtain the decoupled transmission and distribution collaborative scheduling system; Based on the decoupled transmission and distribution collaborative scheduling system, construct new energy output scenarios using cubic sampling, and generate representative scenarios through scenario reduction techniques; Based on the decoupled transmission and distribution collaborative scheduling system and representative scenarios, construct a nuclear-storage collaborative scheduling model; Based on the nuclear-storage collaborative scheduling model, perform joint scheduling on the transmission and distribution collaborative scheduling system; Among them, construct the objective function of the nuclear-storage collaborative scheduling model, solve the objective function of the nuclear-storage collaborative scheduling model to obtain the output of nuclear power units, thermal power units, energy storage devices, and the peak shaving depth of nuclear power units; Based on the output of nuclear power units, thermal power units, energy storage devices, and the peak shaving depth of nuclear power units, perform joint scheduling on the transmission and distribution collaborative scheduling system.

2. The multimodal scheduling method for a power system based on nuclear-storage collaborative optimization according to claim 1, wherein Based on the nuclear-storage collaborative scheduling model, perform joint frequency regulation on the transmission and distribution collaborative scheduling system. The specific process is as follows: Calculate the difference between the grid frequency and the rated frequency to obtain the frequency deviation; Judge whether the frequency deviation is within the primary frequency regulation dead zone. If so, neither the energy storage device nor the nuclear power unit responds; if not, judge whether the frequency deviation is within the small disturbance interval. If so, the energy storage device quickly responds to the frequency regulation command. If not, the energy storage device and the nuclear power unit perform joint abnormal frequency regulation.

3. The multimodal scheduling method for a power system based on nuclear-reservoir collaborative optimization according to claim 1, characterized in that, In the framework of the transmission and distribution collaborative scheduling system, decouple the exchange power of the boundary tie lines of the transmission and distribution collaborative scheduling system.

4. The multimodal scheduling method for a power system based on nuclear-storage collaborative optimization according to claim 1, wherein Construct new energy output scenarios based on Latin hypercube sampling, and generate representative scenarios through scenario reduction techniques. The specific process is as follows: Obtain multiple wind power output scenarios through Latin hypercube sampling; Use the scenario reduction model of Kantorovich distance to reduce multiple wind power output scenarios to obtain representative scenarios.

5. The multimodal scheduling method for a power system based on nuclear-reservoir collaborative optimization according to claim 4, wherein Use the scenario reduction model of Kantorovich distance to reduce multiple wind power output scenarios. The specific process is as follows: Calculate the Kantorovich distance of different wind power output scenarios; Select any scenario, calculate the distance between each scenario and the selected scenario, and multiply it by the probability of the selected scenario. According to the size of the product, delete the scenario with the closest distance to the selected scenario, and update the probability of the set scenario; Repeat the above steps until the scenarios are reduced to the preset number of times.

6. The multimodal scheduling method for a power system based on nuclear-storage collaborative optimization according to claim 1, wherein The constraint conditions include transmission network constraints and distribution network constraints; Among them, the transmission network constraints include power balance constraints, thermal power unit constraints, nuclear power unit constraints, frequency safety constraints, branch power flow constraints, and transmission and distribution network tie line exchange power transmission constraints; The distribution network constraints include power balance constraints, thermal power unit constraints, energy storage state of charge constraints, distribution network power flow constraints, transmission and distribution network tie line exchange power transmission constraints, and comprehensive norm constraints.

7. The multimodal scheduling method for a power system based on nuclear-reservoir collaborative optimization according to claim 1, wherein The objective function of the nuclear-storage collaborative scheduling model is optimized with the minimum total cost of the transmission and distribution network. The formula is: Where: C TA is the operating cost of the transmission grid; k is the number of distribution grids; C DA,k is the operating cost of the k-th distribution grid; N n represents the number of representative scenarios.

8. A multimodal scheduling system for a power system based on coordinated optimization of nuclear and energy storage, characterized in that Including: The transmission and distribution collaborative scheduling system decoupling module is used to decouple the scheduling requirements of the transmission and distribution collaborative scheduling system to obtain the decoupled transmission and distribution collaborative scheduling system; The wind power output scenario generation module is used to construct new energy output scenarios based on the decoupled transmission and distribution coordinated dispatch system by using cubic sampling, and generate representative scenarios through scenario reduction technology; The nuclear-storage coordinated dispatch model joint dispatch module is used to construct a nuclear-storage coordinated dispatch model based on the decoupled transmission and distribution coordinated dispatch system and representative scenarios; Based on the nuclear-storage coordinated dispatch model, conduct joint dispatch on the transmission and distribution coordinated dispatch system; Among them, construct the objective function of the nuclear-storage coordinated dispatch model, solve the objective function of the nuclear-storage coordinated dispatch model, and obtain the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units; Based on the output of nuclear power units, thermal power units, energy storage devices and the peak shaving depth of nuclear power units, conduct joint dispatch on the transmission and distribution coordinated dispatch system.

9. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method described in any one of claims 1-7 above.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it executes the steps of the method described in any one of claims 1-7 above.