Method, system and computer medium for evaluating active power safety margin of power system considering uncertainty of new energy output

Abstract

The present invention discloses a method for evaluating active safety margin of a power system considering the uncertainty of new energy output, comprising the following steps: S1, constructing a first model according to the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; S2, obtaining the active static safety domain boundary according to the first model combined with the maximum volume optimization method; dividing the operation state of the power system into a risk state and a safe state according to the uncertainty of new energy output; S3, evaluating the static active safety margin of the system under the risk state according to the active static safety domain boundary combined with interval mathematics theory; evaluating the static active safety margin of the system under the safe state according to the active static safety domain boundary combined with the safety distance optimization model based on the Lagrange multiplier method. The present invention also provides an active safety margin evaluation system for a power system considering the uncertainty of new energy output.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission network, and in particular to a method, system and computer medium for evaluating active safety margin of a power system taking into account uncertainty of output of new energy sources. Background Art

[0002] Active power, as the core parameter of the power system to measure the power supply capacity, directly affects the stability of the grid frequency and determines whether it can effectively meet the power demand of users. With the continuous increase in the proportion of new energy access, how to make full use of clean energy while ensuring the stability of the power system has become a technical challenge and research hotspot that needs to be solved urgently. The frequency regulation and peak regulation capabilities of the power system face tremendous pressure during high-load periods or large-scale power dispatching. At this time, the impact of fluctuating energy on system stability is particularly significant. Therefore, it is crucial to accurately evaluate the active safety margin of the power system, especially to fully consider the uncertainty of new energy output.

[0003] At present, the active safety margin assessment methods of power systems are mainly divided into two categories: safety assessment methods based on state variables and safety assessment methods based on safety domains.

[0004] The state variable-based assessment method is an important means in the field of power system security assessment. Its core idea is to use the operating state variables of the power system as the basis for assessment and predict the safety of the system through in-depth analysis of these variables. Specifically, the state variable-based assessment method can be divided into two types: probabilistic assessment method and data-driven assessment method. The probabilistic assessment method is to model the uncertainty of renewable energy generation and load based on the probabilistic method, and construct a series of single safety assessment indicators. For example, indicators such as thermal overload probability, voltage over-limit probability and voltage stability probability are used to assess the operational safety of the system. The probabilistic assessment method has a high theoretical value for modeling uncertain factors, but it is often difficult to fully cover the multiple risks in system operation. The data-driven assessment method relies on the rapid development of big data and artificial intelligence technology, takes power flow information such as voltage and power as the characteristic input of the operating mode, and uses deep learning models and deep convolutional neural networks to quickly assess the safety of the power system. This method can handle massive amounts of uncertainty data and is suitable for complex and highly dynamic operating environments. Its advantages are high efficiency and real-time performance, but it depends on the quality of the data and the stability of the algorithm. If the data is biased or the model is improperly designed, the assessment results may be distorted. Existing state variable-based assessment methods rely heavily on a large amount of uncertainty data and complex mathematical models, and the credibility of their results is significantly affected by data quality and model accuracy. In the case of high-dimensional uncertainty in renewable energy output, the reliability of such assessments is often insufficient and cannot effectively quantify the safety margin of the system's current operating state.

[0005] The safety assessment method based on safety domain is mainly based on the static safety domain theory of power system. This method first calculates the boundary of the static safety domain, analyzes the spatial relationship between the system operating point and the boundary of the safety domain, defines the Euclidean distance from the operating point to the boundary of the safety domain as the static safety distance, and then evaluates the safety of the system. Compared with the evaluation method based on state variables, the method based on safety domain pays more attention to the spatial geometric characteristics of the system as a whole and has better interpretability. However, the evaluation of existing safety assessment methods based on safety domain is usually limited to a single operating point. In a power system with a high proportion of new energy access, the system changes from a single operating point to an uncertain operating domain, which may lead to misjudgment of the system safety state and cannot meet the evaluation requirements of the safety margin of the new energy power system.

[0006] Therefore, a new technical solution is urgently needed to solve the technical problem of how to improve the assessment accuracy of the active safety margin assessment method of the power system. Summary of the invention

[0007] The present invention provides a method for evaluating active safety margin of an electric power system taking into account uncertainty of output of new energy sources and a computer medium, so as to solve the technical problem of how to improve the evaluation accuracy of the method for evaluating active safety margin of an electric power system.

[0008] To achieve the above object, the present invention provides a method for evaluating active safety margin of a power system taking into account the uncertainty of output of renewable energy, comprising the following steps:

[0009] S1. Constructing a first model based on the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system.

[0010] S2. According to the first model combined with the maximum volume optimization method, the active static safety domain boundary is obtained; the maximum volume optimization method includes a non-expandable method for optimization through a nonlinear programming model; according to the uncertainty of the output of new energy, the operating state of the power system is divided into a risk state and a safe state.

[0011] S3. According to the active static safety domain boundary combined with interval mathematics theory, the static active safety margin of the system under risk state is evaluated; according to the active static safety domain boundary combined with the safety distance optimization model based on Lagrange multiplier method, the static active safety margin of the system under safe state is evaluated.

[0012] Preferably, S1 comprises:

[0013] S11. Solve the hyperpolyhedron safety region representing the active injection power of all nodes in the power system and The intuitive subdomain of the inscribed super cuboid .

[0014] S12. Based on the hyperpolyhedron security domain and the inscribed super cuboid Get the first model.

[0015] Preferably, S11 includes:

[0016] Assumptions represents the set of all nodes in the power system, , represents the number of nodes in the power system, Indicates nodes; ; Represents the set of load nodes, the number of load nodes is ; Represents the set of generator nodes, the number of generator nodes is , Middle The nodes are balance nodes; Represents the set of all lines, the number of lines is .

[0017] The active power balance relationship can be expressed by the following relationship:

[0018] The phase angle difference constraint at both ends of the transmission line can be expressed by the following relationship:

[0019] The active output constraint of the generator can be expressed by the following relationship:

[0020] in, represents the injected power; , Representation Node The injected power; represents the node susceptance matrix; represents the injected power; , Representation Node The voltage phase angle; It represents the phase difference matrix allowed at both ends of the line, , , Indicates The phase angle difference between the two ends of the line; Represents the association matrix between branches and nodes, and its number of rows is the number of lines in the power system , the number of columns is the number of nodes in the power system , Obtained according to the line topology of the power system; Indicates generator The meritorious contribution, and Respectively represent generators The given maximum and minimum active output values; Indicates transpose.

[0021] The hyperpolyhedron safety domain representing the active injected power of all nodes is It can be expressed by the following relationship:

[0022] Super Polyhedral Security Domain There exists a super cuboid inscribed in the intuitive subdomain , inscribed super cuboid The safety domain can be expressed by the upper and lower limits of the injected power, which can be expressed by the following relationship: in, , Representation Node The lower boundary of the injected power, , Representation Node Upper boundary of the injected power.

[0023] Preferably, S12 includes:

[0024] Assume that the injected power of the system under the given system operation state is , , Indicates the node in the given system running state The corresponding node voltage phase angle matrix is , , Indicates the node in the given system running state The voltage phase angle.

[0025] Then there exists:

[0026] in, It represents the phase angle difference matrix allowed at both ends of the line under the basic operating point, and its value is ; Indicates the line in a given system operating state The phase angle difference between the two ends.

[0027] Hyperpolyhedron security domain and the inscribed super cuboid Expressed by power change, we can get and ;joint and , and the first model is obtained; the first model can be expressed by the following relationship:

[0028] in, represents the change in node injection power, , Representation Node The injection power variation; Indicates the minimum value of the node injection power change, , Representation Node Minimum change in injected power; Indicates the maximum value of the node injection power change,

[0029] , Representation Node Maximum variation of injected power; Indicates The active power increment of each generator; It represents the active power of the generator at the initial operating point.

[0030] Preferably, the active static safety domain boundary obtained according to the first model combined with the maximum volume optimization method includes:

[0031] The first model is transformed into a nonlinear programming model to obtain the second model, which can be expressed by the following relationship:

[0032] in, represents the hypervolume of an inscribed hypercube; Indicates the symbol for continuous multiplication; Represents a generator node Maximum power increment; Represents a generator node The minimum power increment; , is the susceptance matrix No. Line Column elements, is the susceptance matrix No. Line Column elements; and Respectively and The matrix elements; Indicates the output value of the balancing machine in the initial condition; Represents the vector composed of active loads of all nodes, Representation Node Active load; Indicates The first node number of the line, Indicates The end node number of the line; Indicates the maximum output value of the balancing machine; Indicates the minimum output value of the balancing machine; and Indicates the power increment of the generator's active output.

[0033] The second model is solved by the primal-dual interior point method to obtain the active static safety region boundary.

[0034] The active static safety domain boundary includes the upper boundary and the lower boundary, including:

[0035] Upper Boundary: ;

[0036] Lower Boundary: .

[0037] Preferably, the evaluation of the static active safety margin of the system under risk state based on the active static safety domain boundary combined with interval mathematical theory includes:

[0038] Defining interval overlap according to interval mathematics theory ; Represents a security domain. Indicates the interval operation domain; It represents the intersection of the security domain and the interval operation domain, that is, the overlapping domain.

[0039] represents the hypervolume of the overlapping domain; Represents the hypervolume of the interval operation domain.

[0040] Constructing a third model based on linear optimization to solve the hypervolume of the inscribed hypercube with the largest internal volume in the overlapping domain , the third model can be expressed by the following relationship:

[0041] in, represents the active power injection increment of the inscribed super cuboid, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; Represents the hypervolume of the inscribed hypercube inside the overlapping domain.

[0042] Constructing the fourth model based on linear optimization to solve the hypervolume of the circumscribed hypercube with the smallest external volume in the overlapping domain , the fourth model can be expressed by the following relationship:

[0043] in, represents the active power injection increment of the external super-rectangle, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; A hypervolume representing the circumscribed hypercube outside the overlap domain.

[0044] By taking and The average value of the hypervolume is used to approximate the hypervolume of the overlapping domain, which can be expressed by the following relationship:

[0045] Assumptions The vector composed of the maximum values ​​of the active power increment intervals of the generator nodes is , the vector of minimum values ​​is , then there exists:

[0046] according to and Solving the overlap of power systems , which can be expressed by the following relationship: when When it is equal to 0, it means that there is no intersection between the interval operation domain and the safety domain, that is, there is no overlapping domain, the power system is in an unsafe state, and the static active safety margin is 0.

[0047] when When it is greater than 0 and less than 1, it means that part of the interval operation domain overlaps with the safety domain, forming an overlapping domain, and the remaining part is outside the safety domain. The power system is in a risky state, and the value of the static active safety margin is .

[0048] Preferably, the evaluation of the static active safety margin of the system under a safe state according to the active static safety domain boundary combined with the safety distance optimization model based on the Lagrange multiplier method includes:

[0049] When the overlap When it is equal to 1, the power system is in a safe state; define the safe distance Used to evaluate the static active power safety margin of the power system in a safe state; safety distance Includes the shortest distance from the center of the interval operation domain to each boundary point of the safety domain.

[0050] The safety distance optimization model is constructed based on the Lagrange multiplier method, which can be expressed by the following relationship:

[0051] in, ; Represents the introduced column vector of multipliers to be found, which is used to represent the boundary where the points on the safety boundary are located. ; is the variable to be determined, which consists of the coordinates of the points on the boundary of the safety domain.

[0052] make express , Represents an equality constraint , Inequality constraints ; The safety distance optimization model is transformed into an unconstrained optimization problem through the Lagrange multiplier method, which can be expressed by the following relationship:

[0053] in, Symbol for Lagrangian function; , , , All represent Lagrange multipliers; ; ; ; is a one-dimensional vector.

[0054] Solve the unconstrained optimization problem and obtain the minimum distance from the interval operation domain to the safety domain boundary , that is, the safety distance. The active power safety margin is evaluated based on the safety distance as the margin evaluation index to obtain the static active power safety margin when the power system is in a safe state.

[0055] The present invention also provides an active safety margin assessment system for an electric power system taking into account the uncertainty of new energy output, which is used in the method of the present invention. The system includes a model building module, an active static safety domain boundary solving module, an operating status classification module and a safety margin assessment module.

[0056] The model building module is used to build a first model according to the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system.

[0057] The active static safety domain boundary solving module is used to obtain the active static safety domain boundary according to the first model combined with the maximum volume optimization method; the maximum volume optimization method includes a non-expanded method for optimization through a nonlinear programming model.

[0058] The operation status classification module is used to classify the operation status of the power system into risk status and safety status according to the uncertainty of renewable energy output.

[0059] The safety margin assessment module is used to assess the static active safety margin of the system under risk conditions based on the active static safety domain boundary combined with interval mathematics theory. It is also used to assess the static active safety margin of the system under safety conditions based on the active static safety domain boundary combined with a safety distance optimization model based on the Lagrange multiplier method.

[0060] The present invention also provides a computer medium, comprising a processor, a memory and a computer program for implementing the method of the present invention.

[0061] The present invention has the following beneficial effects:

[0062] The method for evaluating the active safety margin of a power system considering the uncertainty of the output of new energy of the present invention constructs a static active safety domain model of the power system according to the active power balance relationship, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator, so that the method of the present invention can more accurately describe the static active safety domain of the power system. The boundary of the active static safety domain is solved by combining the maximum volume optimization method with the static active safety domain model of the power system, so that the method of the present invention greatly simplifies the complex process of directly obtaining the super volume of the overlapping domain, and improves the efficiency of solving the super volume of the overlapping domain. According to the uncertainty of the output of new energy, the operating state of the power system is divided into a risk state and a safe state, which avoids simply classifying the risk state as an unsafe state, increases the accuracy of the evaluation result, improves the engineering applicability of the method, and the system safety margin evaluation result is more accurate when a high proportion of new energy is connected. According to the interval mathematics theory, the static active safety margin of the system under the risk state is evaluated, so that the method overcomes the inaccuracy of using a single operating point to describe the operating state of the system. By using interval mathematics theory and a safety distance optimization model based on the Lagrange multiplier method to evaluate the static active safety margin for the risk state and safety state of the power system respectively, this method overcomes the one-sidedness of a single distance indicator and improves the accuracy of the safety margin evaluation of the power system.

[0063] The power system active safety margin assessment system considering the uncertainty of new energy output of the present invention is used in the method of the present invention and has the same beneficial effects as the method of the present invention.

[0064] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0066] Figure 1 It is a flow chart of a preferred embodiment of the present invention.

[0067] Figure 2 It is a preferred embodiment of the present invention and Schematic diagram of the relationship.

[0068] Figure 3 The preferred embodiment of the present invention is Schematic diagram of the first and last node numbers of a line.

[0069] Figure 4 It is a schematic diagram of overlapping domains of risk status of a power system according to a preferred embodiment of the present invention.

[0070] Figure 5 It is a schematic diagram of an inscribed super cuboid of an overlapping domain according to a preferred embodiment of the present invention.

[0071] Figure 6 It is a schematic diagram of a circumscribed super-cuboid of an overlapping domain according to a preferred embodiment of the present invention.

[0072] Figure 7 is the safety distance of the preferred embodiment of the present invention Schematic diagram.

[0073] Figure 8 It is a schematic diagram of overlapping domains of the power system safety status according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0074] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0075] See also Figure 1 In a preferred embodiment of the present invention, a method for evaluating active safety margin of a power system considering the uncertainty of output of renewable energy is provided, comprising the following steps:

[0076] S1. Constructing a first model based on the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system.

[0077] S1 specifically includes:

[0078] S11. Solve the hyperpolyhedron safety region representing the active injection power of all nodes in the power system and The intuitive subdomain of the inscribed super cuboid S11 specifically includes:

[0079] Assumptions represents the set of all nodes in the power system, , represents the number of nodes in the power system, Indicates nodes; ; Represents the set of load nodes, the number of load nodes is ; Represents the set of generator nodes, the number of generator nodes is , Middle The nodes are balance nodes; Represents the set of all lines, the number of lines is .

[0080] The active power balance relationship can be expressed by the following relationship:

[0081]

[0082] The phase angle difference constraint at both ends of the transmission line can be expressed by the following relationship:

[0083]

[0084] The active output constraint of the generator can be expressed by the following relationship:

[0085] in, represents the injected power; , Representation Node The injected power; represents the node susceptance matrix; represents the injected power; , Representation Node The voltage phase angle; It represents the phase difference matrix allowed at both ends of the line, , , Indicates The phase angle difference between the two ends of the line; Represents the association matrix between branches and nodes, and its number of rows is the number of lines in the power system , the number of columns is the number of nodes in the power system , Obtained according to the line topology of the power system; Indicates generator The meritorious contribution, and Respectively represent generators The given maximum and minimum active output values; Indicates transpose.

[0086] The hyperpolyhedron safety domain representing the active injected power of all nodes is It can be expressed by the following relationship:

[0087] In practical applications, the hyperpolyhedron security domain The defined hyperpolyhedral security domain is an implicit security domain, which makes it difficult to intuitively provide people with the range of active injection power changes of all nodes. There exists a super cuboid inscribed in the intuitive subdomain , and See the relationship Figure 2 .exist Figure 2 middle, and They represent the upper and lower boundaries of the injected active power of node 1, and Respectively represent the upper and lower boundaries of the injected active power of node 2; Represents the active injection power of node 1; represents the active injected power of node 2; Indicates the maximum active injection power value allowed by node 1; Indicates the minimum allowed active injection power value of node 1; Indicates the maximum allowed active injection power value of node 2; Indicates the minimum active injection power value allowed by node 2.

[0088] Inscribed Super Cuboid It is an explicit safety domain, which can facilitate the application of active safety domain engineering. The safety domain can be expressed by the upper and lower limits of the injected power, which can be expressed by the following relationship:

[0089] in, , Representation Node The lower boundary of the injected power, , Representation Node Upper boundary of the injected power.

[0090] S12. Based on the hyperpolyhedron security domain and the inscribed super cuboid A first model is obtained. S12 specifically includes:

[0091] Assume that the injected power of the system under the given system operation state is , , Indicates the node in the given system running state i The corresponding node voltage phase angle matrix is , , Indicates the node in the given system running state The voltage phase angle.

[0092] Then there exists:

[0093] in, It represents the phase angle difference matrix allowed at both ends of the line under the basic operating point, and its value is ; Indicates the line in a given system operating state The phase angle difference between the two ends.

[0094] In actual power systems, the injected power at the power system operation point is usually known. In order to facilitate engineering applications, the hyperpolyhedron safety region is and the inscribed super cuboid Expressed by power change, we can get and ;joint and , and the first model is obtained; the first model can be expressed by the following relationship:

[0095] in, represents the change in node injection power, , Representation Node The injection power variation; Indicates the minimum value of the node injection power change, , Representation Node Minimum change in injected power; Indicates the maximum value of the node injection power change, , Representation Node Maximum variation of injected power; Indicates The active power increment of each generator; It represents the active power of the generator at the initial operating point.

[0096] S2. According to the first model combined with the maximum volume optimization method, the active static safety domain boundary is obtained; the maximum volume optimization method includes a non-expandable method for optimization through a nonlinear programming model; according to the uncertainty of the output of new energy, the operating state of the power system is divided into a risk state and a safe state.

[0097] In order to ensure the maximum active safety region of the inscribed super-long body It is a super polyhedral security domain The feasible subdomain must be verified. Whether each vertex in the region satisfies all constraints. However, since the number of vertices increases exponentially with the number of variables, a necessary and sufficient condition is proposed to solve this problem: in addition to the generator output constraint, if the power flow of each line in the two extreme cases satisfies its upper and lower limit constraints, then the region For polyhedron For simplicity, it is assumed that the active power of the load node is certain, then the safety domain The dimension is only related to the number of generator nodes (except for the balancing nodes), and the variable of the safety domain is only the increment of the active output power of the generator. , whose maximum and minimum values ​​are and .

[0098] According to the first model combined with the maximum volume optimization method, the active static safety domain boundary is obtained, which specifically includes:

[0099] The first model is transformed into a nonlinear programming model to obtain the second model, which can be expressed by the following relationship:

[0100] in, represents the hypervolume of an inscribed hypercube; Indicates the symbol for continuous multiplication; Represents a generator node Maximum power increment; Represents a generator node The minimum power increment; , is the susceptance matrix No. Line Column elements, is the susceptance matrix No. Line Column elements; and Respectively and The matrix The matrix Indicates the output value of the balancing machine in the initial condition; Represents the vector composed of active loads of all nodes, Representation Node Active load of Figure 3 , Indicates The first node number of the line, Indicates The end node number of the line; Indicates the maximum output value of the balancing machine; Indicates the minimum output value of the balancing machine; and The intermediate variable selected to facilitate the writing of the second model represents the power increment of the active output of the generator.

[0101] The second model is solved by the primal-dual interior point method to obtain the active static safety region boundary.

[0102] The active static safety domain boundary includes the upper boundary and the lower boundary, including:

[0103] Upper Boundary: ;

[0104] Lower Boundary: .

[0105] In the preferred embodiment of the present invention, the super-long active safety domain is internally connected Should occupy as much as possible The internal space of The commonly used expansion method to solve the safety domain usually starts from the initial operating point and expands in both directions along each coordinate until the formed area is inscribed in the hyperpolyhedron safety domain. The non-expansion method used in the present invention is to directly inscribe the active safety domain of the super-long body through a nonlinear programming model. The volume of is taken as the objective function for optimization, so that the area containing the most safe operating points can be directly obtained, that is, the true maximum inscribed super-long body active safety domain, and there is no problem of expansion order.

[0106] In a preferred embodiment of the present invention, the operation state of the power system is divided into a risk state and a safety state according to the uncertainty of the output of new energy sources, including:

[0107] The existing safety margin assessment method mainly evaluates the operating point under deterministic scenarios. However, if this method is still used when considering the uncertainty of renewable energy output, the credibility of the assessment results will be reduced. Therefore, the operating state of the power system is divided into risk state and safety state according to the uncertainty of renewable energy output. The active safety margin assessment of the system will also be carried out for risk state and safety state respectively.

[0108] S3. According to the active static safety domain boundary combined with interval mathematics theory, the static active safety margin of the system under risk state is evaluated; according to the active static safety domain boundary combined with the safety distance optimization model based on Lagrange multiplier method, the static active safety margin of the system under safe state is evaluated.

[0109] S3 specifically includes:

[0110] According to the active static safety domain boundary combined with interval mathematics theory, the static active safety margin of the system under risk state is evaluated to obtain the static active safety margin of the power system under risk state. Specifically including:

[0111] Defining interval overlap according to interval mathematics theory ; Indicates the security domain. Indicates the interval operation domain; It represents the intersection of the safety domain and the interval operation domain, that is, the overlapping domain, which is used to evaluate the safety margin under the system risk state. represents the hypervolume of the overlapping domain; Represents the hypervolume of the interval operation domain.

[0112] In the preferred embodiment of the present invention, when the power system is in a risk state, the overlapping domain diagram is shown in FIG. Figure 4 .exist Figure 4 middle, Represents a security domain; Indicates the interval operation domain; Indicates overlapping domains.

[0113] See also Figure 5 , construct the third model based on linear optimization to solve the hypervolume of the inscribed hypercube with the largest internal volume in the overlapping domain .exist Figure 5 middle, represents overlapping domains; Represents the maximum inscribed hypercube of the overlapping domains.

[0114] The third model can be expressed by the following relationship:

[0115] in, represents the active power injection increment of the inscribed super cuboid, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; Represents the hypervolume of the inscribed hypercube inside the overlapping domain.

[0116] See also Figure 6 , construct the fourth model based on linear optimization to solve the hypervolume of the circumscribed hypercube with the smallest external volume in the overlapping domain .exist Figure 6 middle, represents overlapping domains; The smallest circumscribed hypercube that represents the overlapping domain.

[0117] The fourth model can be expressed by the following relationship:

[0118] in, represents the active power injection increment of the external super-rectangle, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; A hypervolume representing the circumscribed hypercube outside the overlap domain.

[0119] By taking and The average value of the hypervolume is used to approximate the hypervolume of the overlapping domain, which can be expressed by the following relationship:

[0120] Assumptions The vector composed of the maximum values ​​of the active power increment intervals of the generator nodes is , the vector of minimum values ​​is , then there exists:

[0121]

[0122] according to and Solving the overlap of power systems , which can be expressed by the following relationship:

[0123]

[0124] when When it is equal to 0, it means that there is no intersection between the interval operation domain and the safety domain, that is, there is no overlapping domain, the power system is in an unsafe state, and the static active safety margin is 0.

[0125] when When it is greater than 0 and less than 1, it means that part of the interval operation domain overlaps with the safety domain, forming an overlapping domain, and the remaining part is outside the safety domain. The power system is in a risky state, and the value of the static active safety margin is .

[0126] In a preferred embodiment of the present invention, a hypervolume approximation method is used to obtain the hypervolume of the overlapping domain, that is, the hypervolume average of the smallest hypercube circumscribed and the largest hypercube inscribed in the overlapping domain is taken to approximate the hypervolume of the overlapping domain. The hypervolume of the smallest hypercube circumscribed and the hypervolume of the largest hypercube inscribed can both be obtained by an optimization method, which greatly simplifies the complex process of directly obtaining the hypervolume of the overlapping domain and improves the efficiency of solving the hypervolume of the overlapping domain. At the same time, the method of taking the hypervolume average of the smallest hypercube circumscribed and the largest hypercube inscribed in the overlapping domain to approximate the hypervolume of the overlapping domain is theoretically supported by mathematical theories of linearization, which guarantees the accuracy of the solved hypervolume results of the overlapping domain to a certain extent.

[0127] According to the active static safety domain boundary combined with the safety distance optimization model based on the Lagrange multiplier method, the static active safety margin of the system in a safe state is evaluated to obtain the static active safety margin of the power system in a safe state. Specifically, it includes:

[0128] When the overlap When it is equal to 1, the power system is in a safe state; see Figure 7 , define the safe distance Used to evaluate the static active power safety margin of the power system in a safe state; safety distance Includes the shortest distance from the center of the interval operation domain to each boundary point of the safety domain. Figure 7 middle, Represents a security domain; Indicates the interval operation domain; Represents a point on the boundary of a security domain; Indicates the center of the interval operation domain; Indicates a safe distance.

[0129] In the preferred embodiment of the present invention, when the power system is safe, the overlapping domain diagram is shown in Figure 8 .exist Figure 8 middle, Represents a security domain; Indicates the interval operation domain; Indicates overlapping domains.

[0130] The safety distance optimization model is constructed based on the Lagrange multiplier method, which can be expressed by the following relationship:

[0131]

[0132] in, ; Represents the introduced column vector of multipliers to be found, which is used to characterize the boundary where the points on the safety boundary are located. ; is the variable to be determined, which consists of the coordinates of the points on the boundary of the safety domain; The coordinates of the representation are determined by the dimension, for example, two-dimensional The coordinates of the horizontal axis and the vertical axis are composed of two dimensions. When the dimension increases The coordinates of correspond to the expanded dimensions.

[0133] make express , Represents an equality constraint , Inequality constraints ; The safety distance optimization model is transformed into an unconstrained optimization problem through the Lagrange multiplier method, which can be expressed by the following relationship:

[0134] in, Symbol for Lagrangian function; , , , All represent Lagrange multipliers; ; ; ; is a one-dimensional vector.

[0135] Solve the unconstrained optimization problem and obtain the minimum distance from the interval operation domain to the safety domain boundary , that is, the safety distance. The active power safety margin is evaluated based on the safety distance as the margin evaluation index to obtain the static active power safety margin when the power system is in a safe state.

[0136] In a preferred embodiment of the present invention, an optimization model is used to solve the safety distance, and a Lagrangian function is constructed to transform the optimization model into an unconstrained nonlinear optimization problem, which can be quickly solved by an existing nonlinear algorithm, greatly improving the efficiency of solving the safety distance.

[0137] In order to evaluate the effectiveness of the method of the present invention, the following two examples are used for verification:

[0138] (1) The static active safety margin of the power system in the risk state and the safe state is evaluated by the method of the present invention, and compared with the margin evaluation method based on a single operating point, using a 6-node test system. The 6-node system adopted includes 8 lines, 3 load nodes and 3 generator nodes. The line and load parameters are shown in Table 1 and Table 2 respectively. All parameters are in per unit value, and the reference power is 100 MVA. One generator in the system is set as a balanced machine, and the other two units are new energy generators. The output is volatile. The fluctuation range of the active output of the generator is set to ±20%. The interior point method is used to solve the safety margin optimization model. The parameters of the interior point method in the example are set as: convergence accuracy , center parameter Through calculation, in this example, the method of the present invention is more accurate and comprehensive than the evaluation result based on the operating point.

[0139]

[0140]

[0141] (2) The engineering applicability of the method of the present invention is verified using the IEEE30 test system. The IEEE30 node example used includes 6 generators, 37 transmission lines, 4 transformers and 2 reactive compensation capacitors. All parameters are in per unit value, and the reference power is 100 MVA. The generators in the system (except the balancing machine) are all new energy generators with fluctuating output. The active output fluctuation range of the new energy generator is ±30%. The parameters of the interior point method in the example are set as: convergence accuracy , center parameter Through calculation, under this example, the method of the present invention can solve the large-node system in different power data fluctuation ranges, and has good robustness and engineering application capabilities.

[0142] In summary, the method for evaluating the active safety margin of the power system considering the uncertainty of the output of new energy of the present invention constructs the static active safety domain model of the power system according to the active power balance relationship, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator, so that the method of the present invention can more accurately describe the static active safety domain of the power system. The boundary of the active static safety domain is solved by combining the maximum volume optimization method with the static active safety domain model of the power system, so that the method of the present invention greatly simplifies the complex process of directly obtaining the super volume of the overlapping domain, and improves the efficiency of solving the super volume of the overlapping domain. According to the uncertainty of the output of new energy, the operating state of the power system is divided into a risk state and a safe state, which avoids simply classifying the risk state as an unsafe state, increases the accuracy of the evaluation result, improves the engineering applicability of the method, and the system safety margin evaluation result is more accurate when a high proportion of new energy is connected. According to the interval mathematics theory, the static active safety margin of the system under the risk state is evaluated, so that the method overcomes the inaccuracy of using a single operating point to describe the operating state of the system. By using interval mathematics theory and a safety distance optimization model based on the Lagrange multiplier method to evaluate the static active safety margin for the risk state and safety state of the power system respectively, this method overcomes the one-sidedness of a single distance indicator and improves the accuracy of the safety margin evaluation of the power system.

[0143] In a preferred embodiment of the present invention, a power system active safety margin assessment system that takes into account the uncertainty of new energy output is also provided, which is used for the method of the present invention. The system includes a model building module, an active static safety domain boundary solving module, an operating status classification module and a safety margin assessment module.

[0144] The model building module is used to build a first model according to the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system.

[0145] The active static safety domain boundary solving module is used to obtain the active static safety domain boundary according to the first model combined with the maximum volume optimization method; the maximum volume optimization method includes a non-expanded method for optimization through a nonlinear programming model.

[0146] The operation status classification module is used to classify the operation status of the power system into risk status and safety status according to the uncertainty of renewable energy output.

[0147] The safety margin assessment module is used to assess the static active safety margin of the system under risk conditions based on the active static safety domain boundary combined with interval mathematics theory. It is also used to assess the static active safety margin of the system under safety conditions based on the active static safety domain boundary combined with a safety distance optimization model based on the Lagrange multiplier method.

[0148] The power system active safety margin assessment system considering the uncertainty of new energy output of the present invention is used in the method of the present invention and has the same beneficial effects as the method of the present invention.

[0149] In a preferred embodiment of the present invention, a computer medium is also provided, including a processor, a memory, and a computer program for implementing the method of the present invention.

[0150] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for evaluating active safety margin of a power system considering uncertainty in output of renewable energy, characterized in that: The following steps are involved: S1. Constructing a first model according to the active power balance relationship of the power system, the phase difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system; S2. Obtaining the active static safety domain boundary according to the first model combined with the maximum volume optimization method; the maximum volume optimization method includes a non-expanded method for optimization through a nonlinear programming model; According to the uncertainty of renewable energy output, the operation status of the power system is divided into risk status and safety status; According to the first model combined with the maximum volume optimization method, the active static safety domain boundary includes: The first model is converted into a nonlinear programming model to obtain a second model, which can be expressed by the following relationship: ， ， ， in, represents the hypervolume of an inscribed hypercube; Indicates the symbol for continuous multiplication; represents a collection of generator nodes; Represents the set of all lines; and Respectively represent generator The given maximum and minimum active output values; Indicates the active power of the generator at the initial operating point; Represents a generator node Maximum power increment; Represents a generator node The minimum power increment; , represents the node susceptance matrix; is the susceptance matrix No. Line Column elements, is the susceptance matrix No. Line Column elements; and Respectively and The matrix elements; It indicates the phase angle difference matrix allowed at both ends of the line; It represents the phase angle difference matrix allowed at both ends of the line under the basic operating point; Indicates the output value of the balancing machine in the initial condition; Represents the vector composed of active loads of all nodes, Representation Node Active load; Indicates The first node number of the line, Indicates The end node number of the line; Indicates the maximum output value of the balancing machine; Indicates the minimum output value of the balancing machine; and Indicates the power increment of the generator's active output; Solving the second model by the primal-dual interior point method to obtain the active static safety region boundary; The active static safety domain boundary includes an upper boundary and a lower boundary, including: Upper Boundary: ; Lower Boundary: ; S3. Evaluate the static active safety margin of the system under risk state according to the active static safety domain boundary combined with interval mathematics theory; evaluate the static active safety margin of the system under safe state according to the active static safety domain boundary combined with a safety distance optimization model based on Lagrange multiplier method.

2. The method for evaluating active power safety margin of a power system considering the uncertainty of output of renewable energy according to claim 1 is characterized in that: The S1 includes: S11. Solve the hyperpolyhedron safety region representing the active injection power of all nodes in the power system and The intuitive subdomain of the inscribed super cuboid ; S12, according to the hyperpolyhedron security domain and the inscribed super cuboid Get the first model.

3. The method for evaluating active safety margin of a power system considering uncertainty of output of renewable energy according to claim 2 is characterized in that: The S11 includes: Assumptions represents the set of all nodes in the power system, , represents the number of nodes in the power system, Indicates nodes; ; Represents the set of load nodes, the number of load nodes is ; Represents the set of generator nodes, the number of generator nodes is , Middle The nodes are balance nodes; Represents the set of all lines, the number of lines is ; The active power balance relationship can be expressed by the following relationship: ， The phase angle difference constraint at both ends of the transmission line can be expressed by the following relationship: ， The generator active output constraint can be expressed by the following relationship: ， in, represents the injected power; , Representation Node The injected power; represents the node susceptance matrix; represents the injected power; , Representation Node The voltage phase angle; It represents the phase difference matrix allowed at both ends of the line, , , Indicates The phase angle difference between the two ends of the line; Represents the association matrix between branches and nodes, and its number of rows is the number of lines in the power system , the number of columns is the number of nodes in the power system , Obtained according to the line topology of the power system; Indicates generator The meritorious contribution, and Respectively represent generator The given maximum and minimum active output values; Indicates transposition; The hyperpolyhedron safety domain representing the active injected power of all nodes is It can be expressed by the following relationship: ， The hyperpolyhedral security domain There exists a super cuboid inscribed in the intuitive subdomain , the inscribed super cuboid The safety domain can be expressed by the upper and lower limits of the injected power, which can be expressed by the following relationship: ， in, , Representation Node The lower boundary of the injected power, , Representation Node Upper boundary of the injected power.

4. The method for evaluating active power safety margin of a power system considering the uncertainty of output of renewable energy according to claim 3 is characterized in that: The S12 includes: Assume that the injected power of the system under the given system operation state is , , Indicates the node in the given system running state The corresponding node voltage phase angle matrix is , , Indicates the node in the given system running state The voltage phase angle; Then there exists: ， ， in, It represents the phase angle difference matrix allowed at both ends of the line under the basic operating point, and its value is ; Indicates the line in a given system operating state The phase angle difference between the two ends; The hyperpolyhedron security domain and the inscribed super cuboid Expressed by power change, we can get and ;joint and , and obtain the first model; the first model can be expressed by the following relationship: ， in, represents the change in node injection power, , Representation Node The injection power variation; Indicates the minimum value of the node injection power change, , Representation Node Minimum change in injected power; Indicates the maximum value of the node injection power change, , Representation Node Maximum variation of injected power; Indicates The active power increment of the generator; It represents the active power of the generator at the initial operating point.

5. The method for evaluating active power safety margin of a power system considering the uncertainty of output of renewable energy according to claim 4 is characterized in that: The static active safety margin assessment of the system under risk state based on the active static safety domain boundary combined with interval mathematical theory includes: Defining interval overlap according to interval mathematics theory ; Represents a security domain. Indicates the interval operation domain; It represents the intersection of the security domain and the interval operation domain, that is, the overlapping domain; A hypervolume representing the overlapping domain; A hypervolume representing the operating domain of the interval; Constructing a third model based on linear optimization to solve the hypervolume of the inscribed hypercube with the largest internal volume in the overlapping domain , the third model can be expressed by the following relationship: ， in, represents the active power injection increment of the inscribed super cuboid, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; The hypervolume representing the inscribed hypercube inside the overlapping domain; Constructing a fourth model based on linear optimization to solve the hypervolume of the circumscribed hypercube with the smallest external volume of the overlapping domain , the fourth model can be expressed by the following relationship: ， in, represents the active power injection increment of the external super-rectangle, and Respectively represent nodes Maximum and minimum values ​​of active injected power increment; A hypervolume representing the circumscribed hypercube outside the overlap domain; By taking and The average value of the hypervolume is used to approximate the hypervolume of the overlapping domain, which can be expressed by the following relationship: ， Assumptions The vector composed of the maximum values ​​of the active power increment intervals of the generator nodes is , the vector of minimum values ​​is , then there exists: ， according to and Solving the overlap of power systems , which can be expressed by the following relationship: ， when When it is equal to 0, it means that there is no intersection between the interval operation domain and the safety domain, that is, there is no overlapping domain, the power system is in an unsafe state, and the static active safety margin is 0; when When it is greater than 0 and less than 1, it means that part of the interval operation domain overlaps with the safety domain, forming an overlapping domain, and the remaining part is outside the safety domain. The power system is in a risky state, and the value of the static active safety margin is .

6. The method for evaluating active power safety margin of a power system considering the uncertainty of output of renewable energy according to claim 5 is characterized in that: The static active safety margin assessment of the system under the safety state is performed according to the active static safety domain boundary combined with the safety distance optimization model based on the Lagrange multiplier method, including: When the overlap When it is equal to 1, the power system is in a safe state; define the safe distance Used to evaluate the static active power safety margin of the power system in a safe state; the safety distance The shortest distance from the center of the interval operation domain to each boundary point of the safety domain; The safety distance optimization model is constructed based on the Lagrange multiplier method, which can be expressed by the following relationship: ， in, ; Represents the introduced column vector of multipliers to be found, which is used to represent the boundary where the points on the safety boundary are located. ; is the variable to be determined, which consists of the coordinates of the points on the boundary of the safety domain; make express , Represents an equality constraint , Inequality constraints ; The safety distance optimization model is transformed into an unconstrained optimization problem through the Lagrange multiplier method, which can be expressed by the following relationship: ， in, Symbol for Lagrangian function; All represent Lagrange multipliers; ; ; ; is a one-dimensional vector; Solve the unconstrained optimization problem and obtain the minimum distance from the interval operation domain to the safety domain boundary , that is, the safety distance, is used as a margin evaluation indicator to perform active safety margin evaluation to obtain a static active safety margin when the power system is in a safe state.

7. A power system active safety margin assessment system considering the uncertainty of new energy output, used in the method described in any one of claims 1 to 6, characterized in that: The system includes a model building module, an active static safety domain boundary solving module, an operation status classification module and a safety margin evaluation module; The model building module is used to build a first model according to the active power balance relationship of the power system, the phase angle difference constraint at both ends of the transmission line and the active output constraint of the generator; the first model includes a static active security domain model of the power system; The active static safety domain boundary solving module is used to obtain the active static safety domain boundary according to the first model combined with the maximum volume optimization method; the maximum volume optimization method includes a non-expanded method optimized by a nonlinear programming model; The operating state classification module is used to classify the operating state of the power system into a risk state and a safe state according to the uncertainty of the output of new energy sources; The safety margin assessment module is used to assess the static active safety margin of the system under risk conditions based on the active static safety domain boundary combined with interval mathematics theory, and is also used to assess the static active safety margin of the system under safety conditions based on the active static safety domain boundary combined with a safety distance optimization model based on the Lagrange multiplier method.

8. A computer medium, characterized in that The invention comprises a processor, a memory and a computer program for implementing the method according to any one of claims 1 to 6.

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