Method for solving new energy power system operation safety domain geometry

Abstract

The invention discloses a method for solving a new energy power system operation security domain geometry, which is used for efficiently solving a new energy power system operation security domain so as to quantitatively evaluate the new energy consumption capability and security boundary in a power system. According to the method, a security domain is modeled into a polyhedral geometric structure formed by boundary hyperplanes, an orthogonal basis generation method is proposed to solve a single boundary hyperplane equation, and a point-hyperplane iterative algorithm based on a dynamic point selection model and a progressive geometric expansion strategy is proposed, so that global solution of geometric boundaries is further realized. A Monte Carlo sampling experiment result verifies the effectiveness of the method, the efficient evaluation of the new energy consumption level and the safety boundary can be realized, and an effective support is provided for the safe operation of a new energy power system.

Description

Technical Field

[0001] The present invention relates to a method for solving the geometry of a new energy power system operation safety domain, and belongs to the field of new energy absorption capacity evaluation and safe operation scheduling of power systems. Background Art

[0002] With the high proportion of renewable energy integrated into the power system, its high uncertainty and volatility pose significant challenges to the safe operation of the power grid. Quantifying and characterizing its safety margins is crucial for improving the system's safe operation. The safety domain method effectively quantifies and characterizes the safety margins of renewable energy and is a mainstream research method for characterizing renewable energy absorption capacity. The new energy safety domain method can theoretically be incorporated into a subdomain representation framework within a multi-constraint parameter space. Essentially, it is a collection of subspaces composed of key operating parameters (such as renewable energy active output and voltage amplitude) within the feasible solution space of the power system's power flow. Its mathematical representation exhibits diverse characteristics depending on the research object.

[0003] Existing technical approaches for linear safety domains fall into two main categories. The first employs a convex hull dual description method to construct a maximum operating boundary model for distributed generation uncertainty. This convex hull form enhances the flexible control dimension of the feasible domain of nonlinear power flows. For example, multi-parameter planning methods achieve rapid boundary search by constructing regional linear mapping relationships, but suffer from a significant decrease in computational efficiency as the parameter combination dimension expands. The second category develops linearized representation methods based on algebraic elimination theory. For example, the Fourier-Motzkin variable elimination method systematically eliminates linear inequality constraint variables to obtain a reduced-dimensional representation. However, its computational complexity grows exponentially with system scale. While it can be accelerated through the Chernivt rule or bit pattern tree structure, it still faces combinatorial explosion in complex network scenarios. As can be seen from the above, while linearized methods offer analytical advantages, they struggle to overcome the computational complexity and efficiency barriers imposed by large-scale systems. Furthermore, the geometric representation of nonlinear safety domains often exhibits implicit features, making explicit modeling difficult. These theoretical limitations severely restrict the application of new energy safety domain methods. New methods are urgently needed to efficiently solve safety domain boundaries and effectively support research on the planning, operation, and optimization of renewable energy in power systems. Summary of the Invention

[0004] In view of the limitations of the above-mentioned prior art, the present invention proposes a method for solving the geometry of the operational safety domain of a new energy power system, and directly obtains the geometric expression of the operational safety domain of the new energy power system by solving all its boundary hyperplanes. This method is essentially based on simple geometric relationships, so it is an easy-to-use method for solving the operational safety domain, which can be used not only in distribution systems but also in transmission systems. The method of the present invention models the safety domain as a polyhedral geometric structure composed of boundary hyperplanes, proposes an orthogonal basis generation method to solve a single boundary hyperplane equation, proposes a dynamic point selection model and a point-hyperplane iterative algorithm based on global geometry, and further realizes the global solution of the geometric boundary. The method of the present invention can achieve accurate and rapid solution of the geometric operational domain of a new energy power system.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for solving the geometry of a new energy power system operation safety domain includes the following steps:

[0007] Step 1: Determine the optimal power flow model of the new energy power system and perform linearization processing on it. The optimal power flow model of the new energy power system specifically includes the node power balance equation, upper and lower limit constraints of power generation output, unit ramp power constraints, voltage amplitude constraints, branch power constraints, etc., thereby obtaining the new energy power system operation security domain model. The geometric expression of the security domain model is specifically a geometric expression based on the combination of boundary hyperplanes;

[0008] Step 2: Based on the new energy operation safety domain model of the power system, determine the boundary hyperplane, and for the geometric expression based on the combination of boundary hyperplanes, solve the geometric expression of one of the boundary hyperplanes based on the orthogonal basis generation method to obtain the boundary hyperplane, specifically: in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, first, based on a line pointing from a given point outside the domain to a given point inside the domain, combine the constraints of the optimal power flow model of the new energy power system to construct a linear optimization problem, and solve the linear optimization problem to obtain a boundary point of the new energy power system operation safety domain; based on the coordinates of the obtained boundary points, construct n-1 linear optimization problems, and solve the optimization problem to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and determine the corresponding boundary hyperplane through these n-1 groups of orthogonal basis vectors.

[0009] Step 3: Find an adjacent hyperplane adjacent to the boundary hyperplane determined in step 2, generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the generated new boundary points can uniquely determine the boundary hyperplane; and solve the new boundary hyperplane using the new out-of-domain points based on the method in step 2;

[0010] Step 4: Based on the progressive geometric expansion iterative process of "given out-of-domain points - solving boundary hyperplanes - generating new out-of-domain points based on adjacency hyperplanes - solving new boundary hyperplanes...", iterate steps 2 and 3 until no new out-of-domain points are generated. At this time, all boundary hyperplane expressions of the global geometry of the new energy power system operation safety domain can be obtained, and the geometry of the new energy power system operation safety domain can be finally obtained.

[0011] In the above technical solution, further, in step 1, the node power balance equation, the upper and lower limit constraints of power generation output, the unit ramp power constraint, the voltage amplitude constraint, and the branch power constraint are respectively:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Where: is the set of nodes in the power system, is the set of generation nodes of traditional generators in the power system (each generation node in the set is equipped with a generator); represents a branch set, Each element of includes the node numbers at both ends of the branch; Refers to the phase angle difference from node i to node j; and are the voltage amplitude and phase angle at node i, respectively; and are the voltage amplitude and phase angle at node j, respectively; and are the conductance and susceptance between node i and node i, respectively; and are the active power and reactive power at node i respectively; the superscript g represents the generator; and are the active power and reactive power generated by the generator at the power generation node i respectively; and are the lower limits of active power and reactive power that can be output by the generator at power generation node i respectively; and Power generation nodes The upper limit of active power and reactive power that the generator can output and are the ramp power limits of the generator at the generating node i for increasing and decreasing, respectively; is the active power generated by the generator at the power generation node i during the last operation; is the branch active power from node i to node j; and are the lower and upper limits of the branch active power from node i to node j respectively;

[0021] The optimal power flow model of the new energy power system is converted into a linear model using a first-order Taylor series expansion approximation method, and the nonlinear terms in the optimal power flow model of the new energy power system are linearized, which is specifically expressed as follows:

[0022]

[0023]

[0024]

[0025] After linearization, the feasible region of the optimal power flow model of the new energy power system is It is projected onto the new energy space to obtain the new energy operation safety domain of the power system;

[0026] The power system new energy operation security domain model is specifically as follows:

[0027]

[0028] Where, Provide a safety domain for the operation of new energy power systems; is the coefficient matrix representing the constraints, is the system's new energy state variable (such as new energy output), and D represents the constant term of the constraint condition;

[0029] In the new energy power system operation safety domain The new energy output points within the company meet the following requirements:

[0030]

[0031] Where x is the system state variable (such as node voltage, phase angle, and branch power flow) excluding new energy.

[0032] Furthermore, in step 2, the purpose of proposing the orthogonal basis generation method OBG is to find the inner point closest to the outer point on the line segment between the inner and outer points. This point is the boundary point of the new energy power system operation safety domain on the inner and outer point line segment.

[0033] The OBG method is specifically described as follows. Its essence is to construct a linear optimization problem:

[0034]

[0035] Since the above optimization problem is a convex programming problem, its solution is the global optimal solution. If If it is an out-of-domain point, the new energy power system operation safety domain Will be in and There is a unique boundary point on the line segment (not and ). If is any given point, but it is unknown whether it is inside or outside the domain. Then, the OBG method can also determine It is the new energy power system operation safety domain For a convex feasible region, any point on the line segment connecting two interior points is still an interior point. Therefore, if and only if Time, point Feasible region of the optimal power flow model for renewable energy power systems . Combined It can be seen that if and only if Sometimes, there are Belongs to the new energy power system operation safety domain Therefore, the OBG method can be used to determine the point yes In-domain or out-domain point: When Time, point for points in the domain; when Time, point for out-of-domain point.

[0036] Furthermore, in step 2, n points are used in n-dimensional space Uniquely determine a hyperplane that satisfies n-1 vectors The proof that is linearly independent is as follows:

[0037] A hyperplane in an n-dimensional linear space can usually be expressed as ,in and are the hyperplane parameter matrix and parameter vector, whose dimensions are n and 1 respectively. is the coordinate of a point in n-dimensional linear space. The hyperplane passing through these n points satisfies , the homogeneous linear equations composed of these n equations are written in matrix form as follows:

[0038]

[0039] Where M is a matrix with n rows and n+1 columns.

[0040] By solving the above homogeneous linear equations, we can determine the hyperplane expression by solving the variables c and d. , where c and d are the non-zero solutions of the homogeneous linear equations. Introducing the matrix ,at this time, The rank of M is consistent with that of .

[0041]

[0042] (1) Prove the sufficiency of the above proposition: If the vector are linearly independent, then we have , which shows that the rank of M is only one dimension less than the dimension of the variables (n+1). Then, the non-zero solution of the homogeneous linear equation can be expressed as ,in is a basic solution. Obviously, the hyperplane expression Pointing to the same unique hyperplane . Therefore, if the vector are linearly independent, then a hyperplane expression will be uniquely determined.

[0043] (2) Prove the necessity of the above problem: If we use n points The hyperplane to be solved is unique, then the form of the non-zero solution set of the above formula is , then the rank of M must be n. .if , then the vector Therefore, if the hyperplane is uniquely determined by these n points, then the vector are linearly independent.

[0044] Furthermore, in step 2, the linear optimization problem is solved to obtain one of the boundary points of the new energy power system operation safety domain. ;

[0045] Based on the obtained boundary points The coordinates of , construct n-1 linear optimization problems, as follows:

[0046] To make the boundary point All of the above proofs are satisfied, and the following constraints can be established for all new boundary points:

[0047]

[0048] Where, is a predetermined boundary point, is the i-th boundary point to be found, For Corresponding to other optimization variables in the system, for and The midpoint of As auxiliary point, For Other optimization variables in the corresponding system;

[0049] By solving the n-1 linear optimization problems, n-1 new boundary points are obtained, and thus n-1 sets of orthogonal basis vectors on the boundary hyperplane are calculated. A new boundary point solving (NBPS) method is proposed to solve the above linear optimization problem, and each new boundary point (assuming it is the i-th boundary point to be solved) is obtained. ), whose main purpose is to ensure the generated vector are all non-zero.

[0050] Furthermore, in step 3, the method for generating new out-of-domain points based on progressive geometric expansion is used to generate new out-of-domain points based on the adjacency hyperplane. The specific method is:

[0051] make represents the operational safety domain of the new energy power system solved previously, and It is not the final safe zone for the operation of new energy power systems. ; Based on a given point outside the domain Solve to get the boundary hyperplane and its corresponding boundary constraints , update the new energy power system operation safety domain ,in, represents the operational safety domain updated in the i-th iteration, represents the operational safety domain solved before the i-th time, Represents the i-th newly added boundary constraint; based on the boundary hyperplane and Generate new out-of-domain points New out-of-domain point Must meet: (1) ,Right now ; (2) (3) is the intersection of n boundary hyperplanes, which are the intersection of hyperplane H and It is composed of n-1 different hyperplanes selected from .

[0052] Furthermore, in step 3, considering the special case that some boundary points obtained based on out-of-domain points cannot successfully uniquely determine the boundary hyperplane, a dynamic point selection model is used to ensure that the newly generated boundary points can generate corresponding boundary hyperplanes, thereby achieving the continuity of the safe domain geometry construction. The dynamic point selection model is used to verify the feasibility of the new out-of-domain points and ensure that the new boundary points generated by them can uniquely determine the boundary hyperplane. The specific process is as follows:

[0053] If the new boundary points are generated based on the new out-of-domain points , if the new boundary point does not satisfy ,in, is the i-axis coordinate of the i-th boundary point to be found, then this new boundary point is called is a “bad” boundary point. Since each new boundary point All are from an out-of-domain point The only point obtained is called the out-of-domain point is a "bad" out-of-domain point. In order to deal with this bad out-of-domain point, the present invention proposes a dynamic point selection model DPA to seek a feasible new out-of-domain point (a feasible new out-of-domain point is obtained from the bad out-of-domain point). The DPA model first solves such an auxiliary point so that it satisfies: (1) It belongs to the new energy power system operation safety domain space; (2) the point is on the line segment between the point outside the bad domain and the previous boundary point; (3) the point is farthest from the previous boundary point. Based on the above ideas, the DPA model first establishes the following linear optimization problem to solve the auxiliary point. The model has a global optimal solution and can effectively solve the auxiliary point.

[0054]

[0055] In the formula represents the previous boundary point, represents a "bad" out-of-domain point, Indicates the scale factor of the reselected line segment, represents any point on the line segment between these two points, Then it represents the auxiliary point (the auxiliary point is located on the previously solved hyperplane); after solving the above optimization problem, the feasible new out-of-domain point can be reselected as and midpoint.

[0056] Furthermore, in step 3, a point-hyperplane iterative algorithm based on global geometry is used to iterate steps 2 and 3 based on the progressive geometric expansion iterative process of "given an out-of-domain point - solving the boundary hyperplane - generating a new out-of-domain point based on the adjacent hyperplane - solving the new boundary hyperplane..." until no new out-of-domain points are generated, thereby obtaining the geometry of the new energy power system operation safety domain. The specific method is as follows:

[0057] Step 1): Initialization process: Generate the initial new energy power system operation safety domain boundary hyperplane set, points within the domain and initial points outside the domain.

[0058] Step 2): Use the OBG method to complete the solution of a single boundary hyperplane: based on a given point in the domain and a given point outside the domain, solve the linear optimization problem to obtain the boundary point on the line connecting the two located in the new energy power system operation safety domain; construct n-1 linear optimization problems based on the boundary point, solve the linear optimization problem, and finally obtain the unique boundary hyperplane expression passing through the boundary point in the new energy power system operation safety domain.

[0059] Step 3): Find an adjacent hyperplane adjacent to the boundary hyperplane determined in step 2), use a new out-of-domain point generation method based on progressive geometric expansion to generate new out-of-domain points based on the adjacent hyperplane, and use the dynamic point selection model DPA to verify the feasibility of the new out-of-domain points to ensure that the new boundary points generated can uniquely determine the boundary hyperplane (to ensure iterative continuity); based on the method in step 2), use the new out-of-domain points to solve and obtain a new boundary hyperplane.

[0060] Step 4): Use the progressive geometric expansion strategy PGE to update the geometric expression of the boundary hyperplane combination and search for new outliers: Based on the new boundary hyperplane obtained in step 3), the new energy power system operation safety domain is updated, and then a new domain outlier point set is generated using the new domain outlier point generation method based on progressive geometric expansion;

[0061] Step 5): Select a new out-of-domain point from the new out-of-domain point set obtained in step 4), and repeat steps 2)-4) until the new out-of-domain point set is an empty set. At this time, the final new energy power system operation safety domain geometry is obtained.

[0062] The present invention also provides a device for solving the geometry of the operation safety domain of a new energy power system, comprising:

[0063] The module for constructing the new energy operation safety domain model of the power system is used to determine the optimal power flow model of the new energy power system and perform linearization processing on it, establish a geometric expression based on the combination of boundary hyperplanes, and thus obtain the new energy operation safety domain model of the power system;

[0064] The boundary hyperplane determination module determines the boundary hyperplane based on the new energy operation safety domain model of the power system, and solves the geometric expression of one of the boundary hyperplanes based on the orthogonal basis generation method for the geometric expression based on the boundary hyperplane combination to obtain the boundary hyperplane. Specifically, in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, first, based on the line connecting a given point outside the domain to a given point inside the domain, a linear optimization problem is constructed in combination with the constraints of the optimal power flow model of the new energy power system, and the linear optimization problem is solved to obtain a boundary point of the new energy power system operation safety domain; based on the coordinates of the obtained boundary points, n-1 linear optimization problems are constructed, and the optimization problems are solved to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and the corresponding boundary hyperplane is determined by these n-1 groups of orthogonal basis vectors;

[0065] A new out-of-domain point and new boundary hyperplane generation module is used to find an adjacent hyperplane adjacent to the boundary hyperplane obtained by the boundary hyperplane determination module, generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the new boundary points generated can uniquely determine the boundary hyperplane; and obtain a new boundary hyperplane based on the boundary hyperplane determination module using the new out-of-domain points.

[0066] The loop iteration module is used to control the iterative operation of the boundary hyperplane determination module and the new out-of-domain point and new boundary hyperplane generation module until no new out-of-domain points are generated, thereby obtaining the geometric body of the new energy power system operation safety domain.

[0067] The present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the method for solving the geometry of the operating safety domain of the new energy power system.

[0068] The present invention also provides a computer-readable storage medium having computer instructions stored thereon, wherein the computer instructions are used to enable a computer to execute the method for solving the geometry of the operating safety domain of the new energy power system.

[0069] The beneficial effects of the present invention are:

[0070] The orthogonal basis generation method proposed in the present invention solves n-1 orthogonal basis vectors based on a known boundary point, and can uniquely determine a hyperplane in an n-dimensional space.

[0071] The proposed method for generating new out-of-domain points based on progressive geometric expansion can generate a new set of out-of-domain points for solving a new hyperplane. Furthermore, the present invention proposes a dynamic point selection model to ensure that the resulting new out-of-domain points uniquely define a hyperplane in n-dimensional space.

[0072] The core of the proposed global geometry-based point-hyperplane iterative algorithm lies in the iterative process of "given an out-of-domain point—solving a boundary hyperplane—generating a new out-of-domain point based on the adjacent hyperplane—solving a new boundary hyperplane...", thereby directly obtaining the expression of the boundary hyperplane of the power system's new energy power system operational safety domain, and ultimately obtaining the geometry of the new energy power system's operational safety domain. The method of the present invention is implemented by directly solving the boundary hyperplane. Therefore, the computational time of this method is mainly affected by the number of boundary hyperplanes in the geometric safety domain, and is less affected by the scale of the power system network. This method is well suited for large-scale new energy power system operational safety domain analysis and research. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 A flowchart illustrating a method for solving the geometry of a new energy power system operating security domain according to an embodiment of the present invention is provided;

[0074] Figure 2 Schematic diagram of the OBG method;

[0075] Figure 3 Schematic diagram of the DPA method;

[0076] Figure 4 Schematic diagram (two-dimensional) of the accuracy analysis of the operation safety domain of the new energy power system using the point-hyperplane-geometric method. Figure 4 (a) is an IEEE 30-node example. Figure 4 (b) is an example of IEEE118 node calculation;

[0077] Figure 5 Schematic diagram (3D) of the accuracy analysis of the operation safety domain of the new energy power system using the point-hyperplane-geometric method. Figure 5 (a) is an IEEE 30-node example. Figure 5 (b) is an example of IEEE118 node calculation. DETAILED DESCRIPTION

[0078] The present invention is further described below with reference to the accompanying drawings and embodiments. Figure 1 shown.

[0079] First, the optimal power flow model of the new energy power system is determined and linearized, and a geometric expression based on the combination of boundary hyperplanes is established to obtain the new energy operation safety domain model of the power system; based on the new energy operation safety domain model of the power system, the boundary hyperplane is determined.

[0080] (1) Before solving the boundary hyperplane, the following initialization work needs to be done:

[0081] 1) Set the initial domain of the new energy power system operation security domain and make the initial domain larger than the real domain: Initialize the new energy power system operation security domain of the power system to ,in is the output power of the new energy at node i The upper bound of . The choice of is flexible and can be the node’s current new energy capacity, future planned capacity, or a preset larger capacity to test the capacity boundary.

[0082] 2) Set the initial point in the domain: Can be set as the coordinate origin by , indicating that the power system is in a safe operating state when no new energy is connected. The advantage of the coordinate origin is that it is also a vertex in the safe operation domain of the new energy power system.

[0083] 3) Set the initial out-of-domain point: Initial out-of-domain point Set to the point in the initial domain that is farthest from the point in the initial domain, that is, the upper limit of each new energy output (to ensure that the point outside the initial domain is feasible), by .

[0084] (2) For the geometric expression based on the combination of boundary hyperplanes, the orthogonal basis generation method (OBG) is used to complete the solution of a single boundary hyperplane: in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, based on the line connecting the given point in the domain and the given point outside the domain, combined with the constraints of the optimal power flow model of the new energy power system, a linear optimization problem is constructed, and the linear optimization problem is solved to obtain a boundary point of the new energy power system operation safety domain located on the line connecting the two; based on the obtained boundary points, n-1 linear optimization problems are constructed, and the optimization problem is solved to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and the corresponding boundary hyperplane is determined by these n-1 groups of orthogonal basis vectors, as shown in the following example. Figure 2 shown.

[0085] (3) Find an adjacent hyperplane adjacent to the boundary hyperplane determined in step (2), generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the generated new boundary points can uniquely determine the boundary hyperplane. When the boundary hyperplane generation fails, that is, a bad point occurs, the dynamic point selection model (DPA) is used to reselect out-of-domain points to ensure iterative continuity: The principle of the DPA model in a two-dimensional system is as follows: Figure 3 As shown, if the new boundary point solved Dissatisfied , is the i-axis coordinate of the i-th boundary point to be found, then this new boundary point is called is a "bad" boundary point, and its corresponding out-of-domain point is called a "bad" out-of-domain point. Figure 3 To give an example of a "bad" outlier case, Figure 3 In (a), EP1 is the previous out-of-domain point, and the boundary hyperplane is generated normally, while Figure 3 In (b), EP2 is a “bad” out-of-domain point. To reselect the out-of-domain point, BP1 is the previous boundary point, BP2 is the "bad" boundary point, BP2 For the out-of-domain point EP2, the corresponding boundary point BP2 on the line segment O-EP2 pointing to O is a vertex. Under this boundary point BP2 (vertex), the new boundary point to be solved must violate the condition Solve for an auxiliary point P2, P2 should satisfy (1) it belongs to Space (i.e., the safe operating domain space of the new energy power system) (2) The point is on the line segment between the "bad" out-of-domain point EP2 and the previous boundary point BP1 (3) The point is farthest from the previous boundary point BP1

[0086]

[0087] In the formula Indicates the previous boundary point BP1, represents the “bad” outlier EP2, Indicates the scale factor of the reselected line segment, represents a point on the line segment between these two points, Then it represents the auxiliary point P2. After solving the above optimization problem, the new out-of-domain point can be reselected as and midpoint.

[0088] Among them, a new out-of-domain point generation method based on progressive geometric expansion (PGE) is used to generate new out-of-domain points based on the adjacency hyperplane. The specific method is: let It represents the operational safety domain of the new energy power system solved previously. It is worth noting that It does not represent the final Based on a given point outside the domain Solve to get the boundary hyperplane and its corresponding boundary constraints After that, update the new energy power system operation safety domain (assuming it is the i-th iteration of the solution process), where, and are the hyperplane parameter matrix and parameter vector respectively, represents the operational safety domain updated in the i-th iteration, represents the operational safety domain solved before the i-th time, Represents the boundary constraint added for the i-th time. Based on the boundary hyperplane and Generate new out-of-domain points Each new out-of-domain point Must meet the following requirements: (1) ,Right now ; (2) (3) is the intersection of n boundary hyperplanes, which are the intersection of hyperplane H and It is composed of n-1 different hyperplanes selected from .

[0089] In view of the large number of boundary hyperplanes, the present invention proposes a new out-of-domain point generation method based on progressive geometric expansion to generate new out-of-domain points. If the number of inequality constraints is m, then we only need to determine whether the hyperplane corresponding to the m-th inequality constraint is the current boundary hyperplane. Then, n−1 different hyperplanes are selected from these greatly reduced adjacent hyperplanes to solve the new out-of-domain points, that is, all the corresponding new out-of-domain points are obtained. The kth boundary hyperplane in ( and are the kth hyperplane parameter matrix and parameter vector respectively) and the current boundary hyperplane is an adjacent face, then there is at least one point such that this point is on the intersection of the boundary hyperplane and it is In the domain, that is, the point satisfies the following constraints:

[0090]

[0091] From the above, we can see that The condition for the kth bounding hyperplane in the equation to be adjacent to the current bounding hyperplane is that the above constraints have a solution. By adding an arbitrary linear objective function (such as a simple sum of the w coordinates) to the above constraints to form a linear optimization problem, we can determine whether it has a solution. The advantage of the new out-of-domain point generation method based on progressive geometric expansion is that as the number of bounding hyperplanes increases, the number of their neighbors does not increase dramatically, thus avoiding large loop calculations.

[0092] (4) Iterate steps (2) and (3) using the point-hyperplane iterative algorithm based on global geometry until no new out-of-domain points are generated. At this point, the complete expression of the new energy power system operation safety domain is obtained, thereby obtaining the geometry of the new energy power system operation safety domain.

[0093] To evaluate the accuracy of the proposed method for solving the geometry of the operational safety region of a renewable energy power system, the present invention utilizes the Monte Carlo method in its embodiments to analyze and verify the error between the proposed method and the feasible region of the optimal power flow model of the renewable energy power system before linearization. The number of random samples for the two-dimensional and three-dimensional renewable energy node access scenarios is 5,000 and 10,000, respectively. Table 1 categorizes the Monte Carlo samples, which are represented by corresponding colored points in the subsequent figures.

[0094] Table 1 Classification of Monte Carlo sample results

[0095] category Colors in the picture meaning 1 Green Dot Simultaneously satisfy the operational safety domain of the new energy power system#timg# and the feasible domain of the optimal power flow model of the new energy power system before linearization#timg# 2 Blue Dot Does not meet the operational safety domain of the new energy power system#timg#, but meets the feasible domain of the optimal power flow model of the new energy power system#timg# 3 Yellow Dot Satisfies the operational safety domain of the new energy power system#timg#, but does not satisfy the feasible domain of the optimal power flow model of the new energy power system#timg# 4 Red Dot At the same time, it does not meet the new energy power system operation safety domain #timg# and the new energy power system optimal power flow model feasible domain safety domain #timg#

[0096] Figure 4 The results of the new energy power system operation safety domain in a two-dimensional case (i.e., when two nodes are connected to new energy) are shown. The green shaded area surrounded by the black solid line is the solved new energy power system operation safety domain. As shown in the figure, the geometric safety domains formed by the IEEE 30-node system and the 118-node system are similar. The low proportion of yellow points in the figure indicates that in these two two-dimensional system examples, the new energy power system operation safety domain is met. The point satisfies the feasible region of the optimal power flow model of the new energy power system before linearization Some of the blue dots in the figure are the safety zones of new energy power system operation. The feasible region of the optimal power flow model of the new energy power system before linearization The main manifestation of error is shown in the figure. The number of blue points for the IEEE 30-bus and 118-bus systems is relatively small, indicating relatively small errors relative to the feasible region of the optimal power flow model for the renewable energy power system before linearization. This verifies the accuracy of the operational safety region of the renewable energy power system solved by this method. Furthermore, the number and error of boundary hyperplanes solved for the IEEE 118-bus system are not higher than those for the IEEE 30-bus system, indicating that the error in the operational safety region of the renewable energy power system and the number of boundary hyperplanes solved are less affected by system size.

[0097] Figure 5 The results for the operational safety domain of a new energy power system in a three-dimensional scenario (i.e., with three nodes connected to renewable energy) are shown. The light blue solid area enclosed by the black solid line represents the operational safety domain of the new energy power system. Similar to the two-dimensional case, the number of yellow and blue points in the figure is relatively small. This means that in the three-dimensional scenario, the error between the operational safety domain of the new energy power system and the feasible region of the optimal power flow model of the new energy power system before linearization is also relatively small, further verifying the effectiveness of the proposed operational safety domain of the new energy power system in three dimensions. In addition, a comparison of the two systems shows that the number and error of boundary hyperplanes solved for the 118-node system are not significantly higher than those for the IEEE 30-node system. This further demonstrates that the error in the operational safety domain of the new energy power system and the number of boundary hyperplanes solved are less affected by system scale. Even in more complex high-dimensional scenarios, the method maintains its relatively stable characteristics.

[0098] An embodiment of the present invention further provides a device for solving the geometry of a new energy power system operation security domain, the device comprising:

[0099] The module for constructing the new energy operation safety domain model of the power system is used to determine the optimal power flow model of the new energy power system and perform linearization processing on it, establish a geometric expression based on the combination of boundary hyperplanes, and thus obtain the new energy operation safety domain model of the power system;

[0100] The boundary hyperplane determination module determines the boundary hyperplane based on the new energy operation safety domain model of the power system, and solves the geometric expression of one of the boundary hyperplanes based on the orthogonal basis generation method for the geometric expression based on the boundary hyperplane combination to obtain the boundary hyperplane. Specifically, in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, first, based on the line connecting a given point outside the domain to a given point inside the domain, a linear optimization problem is constructed in combination with the constraints of the optimal power flow model of the new energy power system, and the linear optimization problem is solved to obtain a boundary point of the new energy power system operation safety domain; based on the coordinates of the obtained boundary points, n-1 linear optimization problems are constructed, and the optimization problems are solved to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and the corresponding boundary hyperplane is determined by these n-1 groups of orthogonal basis vectors;

[0101] A new out-of-domain point and new boundary hyperplane generation module is used to find an adjacent hyperplane adjacent to the boundary hyperplane obtained by the boundary hyperplane determination module, generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the new boundary points generated can uniquely determine the boundary hyperplane; and obtain a new boundary hyperplane based on the boundary hyperplane determination module using the new out-of-domain points.

[0102] The loop iteration module is used to control the iterative operation of the boundary hyperplane determination module and the new out-of-domain point and new boundary hyperplane generation module until no new out-of-domain points are generated, thereby obtaining the geometric body of the new energy power system operation safety domain.

[0103] The present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the method for solving the geometry of the operating safety domain of the new energy power system.

[0104] The present invention also provides a computer-readable storage medium having computer instructions stored thereon, wherein the computer instructions are used to enable a computer to execute the method for solving the geometry of the operating safety domain of the new energy power system.

Claims

1. A method for solving the geometry of the safety domain of the operation of a new energy power system, characterized in that: The following steps are involved: Step 1: Determine the optimal power flow model of the renewable energy power system and perform linearization on it, establish a geometric expression based on the combination of boundary hyperplanes, and thus obtain the renewable energy operation security domain model of the power system; Step 2: Based on the new energy operation safety domain model of the power system, determine the boundary hyperplane, and for the geometric expression based on the combination of boundary hyperplanes, solve the geometric expression of one of the boundary hyperplanes based on the orthogonal basis generation method to obtain the boundary hyperplane, specifically: in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, first, based on a line connecting a given point outside the domain to a given point inside the domain, combine the constraints of the optimal power flow model of the new energy power system to construct a linear optimization problem, solve the linear optimization problem to obtain a boundary point of the new energy power system operation safety domain; based on the coordinates of the obtained boundary points, construct n-1 linear optimization problems, solve the optimization problem to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and determine the corresponding boundary hyperplane through these n-1 groups of orthogonal basis vectors; Step 3: Find an adjacent hyperplane adjacent to the boundary hyperplane determined in step 2, generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the generated new boundary points can uniquely determine the boundary hyperplane; and solve the new boundary hyperplane using the new out-of-domain points based on the method in step 2; Step 4: Iterate steps 2 and 3 until no new out-of-domain points are generated, and obtain the geometry of the new energy power system operation safety domain.

2. A method for solving the geometry of the operation safety domain of a new energy power system according to claim 1, characterized in that: In step 1), the optimal power flow model of the new energy power system includes node power balance equations and constraints. The constraints specifically include upper and lower limit constraints of generator output, unit ramp power constraints, voltage amplitude constraints, and branch power constraints. Specifically expressed as: ； ； ； ； ； ； ； ； Where: is the set of nodes in the power system, It is a collection of power generation nodes of traditional generators in the power system; represents a branch set, Each element of includes the node numbers at both ends of the branch; Refers to the phase angle difference from node i to node j; and are the voltage amplitude and phase angle at node i, respectively; and are the voltage amplitude and phase angle at node j, respectively; and are the conductance and susceptance between node i and node i, respectively; and are the active power and reactive power at node i respectively; the superscript g represents the generator; and are the active power and reactive power generated by the generator at the power generation node i respectively; and are the lower limits of active power and reactive power that can be output by the generator at power generation node i respectively; and Power generation nodes The upper limit of active power and reactive power that the generator can output and are the ramp power limits of the generator at the generating node i for increasing and decreasing, respectively; is the active power generated by the generator at the power generation node i during the last operation; is the branch active power from node i to node j; and are the lower and upper limits of the branch active power from node i to node j respectively; The optimal power flow model of the new energy power system is converted into a linear model using a first-order Taylor series expansion approximation method, and the nonlinear terms in the optimal power flow model of the new energy power system are linearized, which is specifically expressed as follows: ； ； ； After linearization, the feasible region of the optimal power flow model of the new energy power system is It is projected onto the new energy space to obtain the new energy operation safety domain of the power system; The power system new energy operation security domain model is specifically as follows: ； Where, Provide a safety domain for the operation of new energy power systems; is the coefficient matrix representing the constraints, is the system's new energy state variable, and D represents the constant term of the constraint condition; In the new energy power system operation safety domain The new energy output points within the company meet the following requirements: Where x is the system state variable excluding new energy.

3. A method for solving the geometry of the operation safety domain of a new energy power system according to claim 2, characterized in that: In step 2: The linear optimization problem is constructed based on a line connecting a given point outside the domain to a given point inside the domain, combined with the constraints of the optimal power flow model of the new energy power system, specifically: ； Where, Represents a given point outside the domain, specifically any given new energy output point outside the domain; Represents a given point in the domain, specifically any new energy output point in a given domain; represents the line segment scale coefficient, express and Any point on the connected line segment; Solve the linear optimization problem to obtain one of the boundary points on the boundary of the new energy power system operation safety domain ; Based on the obtained boundary points The coordinates of , construct n-1 linear optimization problems, specifically: ； Where, is a predetermined boundary point, is the i-th boundary point to be found, For Corresponding to other optimization variables in the system, for and The midpoint of As auxiliary point, For Other optimization variables in the corresponding system; By solving the n-1 linear optimization problems, n-1 new boundary points are obtained, thereby calculating and obtaining n-1 groups of orthogonal basis vectors on the boundary hyperplane.

4. A method for solving the geometry of the operation safety domain of a new energy power system according to claim 3, characterized in that: In step 3, the method for generating new out-of-domain points based on progressive geometric expansion is used to generate new out-of-domain points based on the adjacency hyperplane. The specific method is: make represents the operational safety domain of the new energy power system solved previously, and It is not the final safe zone for the operation of new energy power systems. ; Based on a given point outside the domain Solve to get the boundary hyperplane and its corresponding boundary constraints , update the new energy power system operation safety domain ,in, and are the hyperplane parameter matrix and parameter vector respectively, represents the operational safety domain updated in the i-th iteration, represents the operational safety domain solved before the i-th time, Represents the i-th newly added boundary constraint; based on the boundary hyperplane and Generate new out-of-domain points New out-of-domain point Must meet: (1) ,Right now ; (2) (3) is the intersection of n boundary hyperplanes, which are the intersection of hyperplane H and It is composed of n-1 different hyperplanes selected from .

5. A method for solving the geometry of the operation safety domain of a new energy power system according to claim 4, characterized in that: In step 3, the feasibility of the new out-of-domain point is checked to ensure that the new boundary point generated can uniquely determine the boundary hyperplane, specifically: If the new boundary points are generated based on the new out-of-domain points Dissatisfied ,in, is the i-axis coordinate of the i-th boundary point to be found, then it is called the new boundary point is a "bad" boundary point, and its corresponding out-of-domain point is called a "bad" out-of-domain point. The "bad" out-of-domain point is infeasible, so the dynamic point selection model is used to reselect the out-of-domain point. The specific method is: Based on the "bad" out-of-domain point, an auxiliary point is solved, which satisfies: (1) It belongs to the new energy power system operation safety domain Space (2) The point is on the line segment between the "bad" out-of-domain point and the previous boundary point (3) The point is farthest from the previous boundary point; the specific representation is as follows: ； In the formula represents the previous boundary point, represents a "bad" out-of-domain point, Indicates the scale factor of the reselected line segment, represents any point on the line segment between these two points, Indicates auxiliary points; After solving the above optimization problem, and The midpoint of is taken as a feasible new out-of-domain point.

6. A method for solving the geometry of the operation safety domain of a new energy power system according to claim 4, characterized in that: In step 4, a point-hyperplane iterative algorithm based on global geometry is used to iterate steps 2 and 3 until no new out-of-domain points are generated, thereby obtaining the geometry of the new energy power system operation safety domain. The specific method is as follows: Step 1): Initialization process: Generate the initial new energy power system operation safety domain boundary hyperplane set, points within the domain and initial points outside the domain; Step 2): Use the orthogonal basis generation method to complete the solution of a single boundary hyperplane: Based on a given point in the domain and a given point outside the domain, solve the linear optimization problem to obtain the boundary point on the line connecting the two points located in the new energy power system operation safety domain, construct n-1 linear optimization problems based on the boundary points, solve the linear optimization problems, and finally obtain the unique boundary hyperplane expression passing through the boundary point in the new energy power system operation safety domain; Step 3): Find an adjacent hyperplane adjacent to the boundary hyperplane determined in step 2), generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and use a dynamic point selection model to verify the feasibility of the new out-of-domain points to ensure that the generated new boundary points can uniquely determine the boundary hyperplane; based on the method in step 2, use the new out-of-domain points to solve and obtain a new boundary hyperplane; Step 4): Update the geometric expression of the boundary hyperplane combination and search for new external points: Based on the new boundary hyperplane obtained in step 3), the new energy power system operation safety domain is updated, and then a new domain external point set is generated by a new domain external point generation method based on progressive geometric expansion; Step 5: Select a new out-of-domain point from the new out-of-domain point set obtained in step 4) and repeat steps 2)-4) until the new out-of-domain point set is an empty set. At this time, the final new energy power system operation safety domain geometry is obtained.

7. A device for solving the geometry of the safety domain of operation of a new energy power system, characterized in that: include: The module for constructing the new energy operation safety domain model of the power system is used to determine the optimal power flow model of the new energy power system and perform linearization processing on it, establish a geometric expression based on the combination of boundary hyperplanes, and thus obtain the new energy operation safety domain model of the power system; The boundary hyperplane determination module determines the boundary hyperplane based on the new energy operation safety domain model of the power system, and solves the geometric expression of one of the boundary hyperplanes based on the orthogonal basis generation method for the geometric expression based on the boundary hyperplane combination to obtain the boundary hyperplane. Specifically, in the n-dimensional space determined by n new energy access nodes, for any boundary hyperplane, first, based on the line connecting a given point outside the domain to a given point inside the domain, a linear optimization problem is constructed in combination with the constraints of the optimal power flow model of the new energy power system, and the linear optimization problem is solved to obtain a boundary point of the new energy power system operation safety domain; based on the coordinates of the obtained boundary points, n-1 linear optimization problems are constructed, and the optimization problems are solved to obtain n-1 groups of orthogonal basis vectors on the boundary hyperplane, and the corresponding boundary hyperplane is determined by these n-1 groups of orthogonal basis vectors; A new out-of-domain point and new boundary hyperplane generation module is used to find an adjacent hyperplane adjacent to the boundary hyperplane obtained by the boundary hyperplane determination module, generate new out-of-domain points based on the adjacent hyperplane using a new out-of-domain point generation method based on progressive geometric expansion, and verify the feasibility of the new out-of-domain points to ensure that the generated new boundary points can uniquely determine the boundary hyperplane; Based on the boundary hyperplane determination module, a new boundary hyperplane is obtained by solving the new out-of-domain points; The loop iteration module is used to control the iterative operation of the boundary hyperplane determination module and the new out-of-domain point and new boundary hyperplane generation module until no new out-of-domain points are generated, thereby obtaining the geometric body of the new energy power system operation safety domain.

8. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having computer instructions stored thereon, characterized in that: The computer instructions are used to enable a computer to execute the steps of the method according to any one of claims 1 to 6.

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