Data-driven cross-section non-exceeding transmission power boundary multi-level accurate characterization method

Abstract

The application relates to the technical field of power systems, and particularly discloses a data-driven section-crossing transmission power boundary multi-stage accurate characterization method, which comprises the following steps: step S1, adopting a clustering algorithm based on a Gaussian mixture model, performing unsupervised learning on power grid operation mode data to generate operation mode sub-mode cluster sets; step S2, in each sub-mode cluster set, calculating the initial boundary of a single section according to a conservativeness principle; step S3, searching for the instability domain boundary by using an Alpha Shape algorithm, constructing a coupling boundary, and performing a set operation on the initial boundary to form the final section-crossing transmission power boundary constraint. The application has the advantages that the power grid operation mode is divided into multiple sub-mode cluster sets, a section-crossing transmission power conservativeness calculation method in the operation mode cluster set is proposed, and the problem of excessive conservativeness of a traditional single section-crossing transmission power calculation method is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a data-driven multi-level precise characterization method for a section's non-crossing transmission power boundary. Background Art

[0002] The uneven distribution of energy resources across different countries and regions, coupled with significant differences in energy structures and load demands, has led to an imbalance between supply and demand. For example, China's energy resources are largely concentrated in the higher-elevation, less-developed western region, while load demand is concentrated in the economically developed and densely populated central and eastern coastal regions. This imbalance in energy resource allocation has made large-scale grid interconnection an inevitable development trend in modern power systems. Cross-border grid interconnection has even been achieved in countries and regions such as Europe, Africa, and North America. With the rapid development of my country's power grids from interprovincial to cross-regional, and the continuous construction and commissioning of ultra-high voltage AC and DC transmission channels, the country has achieved a strategic layout of "west-to-east power transmission, north-south power supply, and nationwide interconnection." However, the safety risks of cross-regional power transmission cannot be ignored. Long-distance transmission channels have become a weak link in the power grid, and the risk of instability arises when transmitting high power.

[0003] Calculating transmission channel transmission limits relies on calculating the total transfer capacity (TTC) under typical operating scenarios. The most conservative value is used as a "checkpoint" for project scheduling and operation to ensure absolutely safe and stable grid operation. This "checkpoint" is the section limit, also known as the "no-crossing" power limit for system operation. In small systems, TTC and section no-crossing power limits may be unified due to the limitations of typical scenarios. With the increasing penetration of renewable energy, a "combinatorial explosion" of grid operating modes has occurred, making typical scenarios difficult to identify and TTC calculations challenging. While artificial intelligence solutions exist, their "black box" nature, with its poor interpretability, has limited their widespread trust in the engineering community. As grid operation becomes increasingly complex, the calculation of no-crossing power limits in engineering projects still relies on the experience of grid experts and manual simulations. To ensure absolute safety, no-crossing power limits are often overly conservative, hindering renewable energy integration. Furthermore, these calculations are labor-intensive and low-precision. Some studies have proposed a method for calculating transmission power in tiers that cannot be crossed to tap the transmission potential, but the tiering is still based on expert experience and historical operating methods, which makes it difficult to adapt to systems with a high proportion of new energy.

[0004] In general, the existing methods of non-crossable transmission power grading and conditional mapping provide a direction for tapping the transmission potential of sections. However, there is still a lack of systematic and scientific computational theory on how to effectively reduce the computational complexity, how to consider the joint distribution information of multiple sections, and how to calculate the accurate coupled non-crossable transmission power boundary. Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a data-driven multi-level accurate characterization method for ensuring that a cross-section cannot cross the transmission power boundary.

[0006] The object of the present invention is achieved by the following technical solution: a data-driven multi-level accurate characterization method for a cross-section that cannot cross the transmission power boundary, the method comprising the following steps:

[0007] Step S1: Using a clustering algorithm based on a Gaussian mixture model to perform unsupervised learning on the grid operation mode data to generate operation mode sub-mode clusters;

[0008] Step S2: in each sub-pattern cluster, calculate the initial boundary of a single section according to the conservative principle;

[0009] Step S3: Use the Alpha Shape algorithm to search for the boundary of the instability region, construct a coupling boundary, and calculate the union with the initial boundary to form the final non-crossable transmission power boundary constraint.

[0010] Specifically, the clustering algorithm of the Gaussian mixture model is used to decompose the operation mode sample space into several models based on the Gaussian probability density function, including an N-dimensional Gaussian mixture model with K components, as shown in the following formula:

[0011]

[0012] Among them, N(x|μ k ,∑ k ) is the N-dimensional Gaussian probability density function; μ k represents the mean vector; is the set of operating modes; k is the N×N dimensional covariance matrix; p(x) is the probability density function of the Gaussian mixture model; w k is the mixing weight, which represents the weight coefficient of the kth single Gaussian function in the GMM in the mixing model; x is the operation mode sample vector set, where the vector x i Including traditional unit active output P G , Active power output of new energy units P Re , load active power P Load and DC transmission P DC .

[0013] Specifically, when performing cluster analysis, the maximum likelihood function is used for parameter estimation:

[0014]

[0015] Among them, L(X|θ) is the likelihood function, and the parameter θ that makes L(X|θ) reach the maximum value is obtained through the maximum likelihood function.* ,θ * =argmaxL(X|θ),θ=(μ k ,∑ k ,w k ), finally, we get the cluster of operation mode sub-modes Specifically, when performing parameter estimation, the EM algorithm is used for calculation. The specific method is:

[0016] According to the specified μ k ,∑ k and w k Initial value, calculate the probability that each data point belongs to different categories, data point x j The posterior probability of belonging to class k is:

[0017]

[0018] According to the obtained posterior probability results, the maximum likelihood method is used to obtain the new μ k ,∑ k and w k , the calculation formula is as follows:

[0019]

[0020] Repeatedly calculate the posterior probability and the new μ k ,∑ k and w k , until the log-likelihood function meets the convergence condition |lnL(X|θ) (t) -lnL(X|θ) (t-1) ∣<ε, get the Gaussian mixture model parameter value.

[0021] Specifically, the initial insurmountable transmission power boundary of a single section in each operation mode sub-mode cluster is calculated as follows:

[0022]

[0023] in, For the expected accident set; A collection of clusters of different modes of operation; is the jth operating mode sub-mode cluster; is the safety label of the i-th working condition after the h-th anticipated accident safety and stability verification, 0 means unsafe, and 1 means otherwise; P (i) is the section transmission power under the i-th working condition; P is,j , P se,j They are the minimum active power flow of the section in the unstable operation mode and the maximum active power flow of the section in the stable operation mode in the jth operation mode sub-mode cluster.

[0024] Specifically, the specific steps of step S3 include:

[0025] Step S31, input cross-section power sample data: S = [point j,1 ,…,point j,m ], Boundary adhesion control parameter: α>0;

[0026] Step S32: Construct Delaunay triangulation, calculate the Delaunay triangulation of the power sample data S, generate a set of triangles and their edge sets, and record T = {Δ1, Δ2, ..., Δ m} is the set of all triangles in the triangulation;

[0027]

[0028] Where Conv(S) represents the convex hull of the power sample data S;

[0029] Step S33, calculate the empty sphere radius of all Delaunay edges, for each edge e=(point i ,point j ), calculate the circumscribed circle radius r of each triangle, and take the smallest r as the radius of the empty sphere;

[0030] Step S34: For each edge e=(point i ,piont j ), if the radius of the empty sphere Then keep e; otherwise delete it;

[0031] Step S35: Connect all the retained edges to form the boundary of the Alpha Shape. The remaining boundary points constitute the final boundary polygon, which is recorded as

[0032] Step S36, the initial boundary generated by formula (5) Find the union to form the transmission power boundary constraint that cannot be crossed: Ω j is the unstable operation mode set in operation mode cluster j; Represents the approximation to Ω j Conservative non-transgressable transmission power bounds of the set true bounds;

[0033] Step S37: Output the multi-section transmission power boundary under the current mode type.

[0034] The present invention has the following advantages:

[0035] The proposed method incorporates additional operational characteristics, dividing the grid's operating modes into multiple sub-mode clusters. This method proposes a conservative calculation method for the no-crossing power within each operating mode cluster, addressing the overly conservative nature of traditional single no-crossing power calculation methods. Furthermore, by considering the coupling relationships between multiple sections, a method for calculating the no-crossing power boundary is constructed to accurately characterize the no-crossing power boundary, fully tapping the transmission potential of each section. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the characterization method of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings, but the scope of protection of the present invention is not limited to the following. Figure 1 As shown, a data-driven multi-level precise characterization method for the non-crossable transmission power boundary of a section is provided, which includes the following steps: Step S1, using a clustering algorithm based on a Gaussian mixture model to perform unsupervised learning on the power grid operation mode data to generate operation mode sub-mode clusters; using the clustering algorithm to learn the similarities and differences between the operation modes from massive samples to identify typical patterns of characteristics such as load, DC and new energy, and calculating the non-crossable transmission power in each sub-mode cluster, thereby exploring the transmission potential under a specific operation mode, and indirectly characterizing the non-crossable transmission power boundary more accurately in a higher-dimensional feature space.

[0038] Step S2: in each sub-pattern cluster, calculate the initial boundary of a single section according to the conservative principle;

[0039] Step S3: Use the Alpha Shape algorithm to search for the boundary of the instability region, construct a coupling boundary, and calculate the union with the initial boundary to form the final non-crossable transmission power boundary constraint.

[0040] Furthermore, a clustering algorithm based on a Gaussian mixture model is used to decompose the operation mode sample space into several models based on Gaussian probability density functions, including an N-dimensional Gaussian mixture model with K components, as shown in the following formula:

[0041]

[0042] Among them, N(x|μ k ,∑ k ) is the N-dimensional Gaussian probability density function; μ k represents the mean vector; is the set of operating modes; k is the N×N dimensional covariance matrix; p(x) is the probability density function of the Gaussian mixture model; w kis the mixing weight, which represents the weight coefficient of the kth single Gaussian function in the GMM in the mixing model; x is the operation mode sample vector set, where the vector x i Including traditional unit active output P G , Active power output of new energy units P Re , load active power P Load and DC transmission P DC .

[0043] Furthermore, when performing cluster analysis, the maximum likelihood function is used for parameter estimation:

[0044]

[0045] Among them, L(X|θ) is the likelihood function, and the parameter θ that makes L(X|θ) reach the maximum value is obtained through the maximum likelihood function. * ,θ * =argmaxL(X|θ),θ=(μ k ,∑ k ,w k ), finally, we get the cluster of operation mode sub-modes Furthermore, when performing parameter estimation, the EM algorithm is used for calculation. The specific method is:

[0046] Expected step (E-step): According to the specified μ k ,∑ k and w k Initial value, calculate the probability that each data point belongs to different categories, data point x j The posterior probability of belonging to class k is:

[0047]

[0048] Maximization step (M-step): Based on the obtained posterior probability results, the new μ is obtained using the maximum likelihood method k ,∑ k and w k , the calculation formula is as follows:

[0049]

[0050] Repeat the calculation of E-step and M-step until the log-likelihood function meets the convergence condition |lnL(X|θ) (t) -lnL(X|θ) (t-1) ∣<ε, get the Gaussian mixture model parameter value.

[0051] The GMM clustering algorithm is used to obtain clusters of operating mode sub-modes. The conservative principle is then followed within each cluster to calculate the non-crossable transmission power of sections. For multi-section non-crossable transmission power with coupling effects, if the correlation between sections is not considered, the feasible domain of the multi-section non-crossable transmission power division may be reduced, or even lead to the problem of no feasible method. Therefore, it is necessary to describe the multi-section non-crossable transmission power with logical association constraints based on the consideration of correlation, and perform coupled non-crossable transmission power boundary calculations on related sections. Specifically, this can be divided into initial boundary and coupled boundary calculations. The initial boundary calculation of a single section in each operating mode sub-mode cluster is shown in the following formula:

[0052]

[0053] in, is the set of anticipated accidents, including static, transient and Nk faults; A collection of clusters of different modes of operation; is the jth operating mode sub-mode cluster; is the safety label of the i-th working condition after the h-th anticipated accident safety and stability verification, 0 means unsafe, and 1 means otherwise; P (i) is the section transmission power under the i-th working condition; P is,j , P se,j They are the minimum active power flow of the section in the unstable operation mode and the maximum active power flow of the section in the stable operation mode in the jth operation mode sub-mode cluster.

[0054] Furthermore, the specific steps of step S3 include:

[0055] Step S31: Input cross-sectional power sample data: Boundary adhesion control parameter: α>0;

[0056] Step S32: Construct Delaunay triangulation, calculate the Delaunay triangulation of the power sample data S, generate a set of triangles and their edge sets, and record T = {Δ1, Δ2, ..., Δ m} is the set of all triangles in the triangulation;

[0057]

[0058] Where Conv(S) represents the convex hull of the power sample data S;

[0059] Step S33, calculate the empty sphere radius of all Delaunay edges, for each edge e=(point i ,point j), calculate the circumscribed circle radius r of each triangle, and take the smallest r as the radius of the empty sphere;

[0060] Step S34: For each edge e=(point i ,point j , if the radius of the empty sphere is Then keep e; otherwise delete it;

[0061] Step S35: Connect all the retained edges to form the boundary of the Alpha Shape. The remaining boundary points constitute the final boundary polygon, which is recorded as

[0062] Step S36, the initial boundary generated by formula (5) Find the union to form the transmission power boundary constraint that cannot be crossed: Ω j is the unstable operation mode set in operation mode cluster j; Represents the approximation to Ω j Conservative non-transgressable transmission power bounds of the set true bounds;

[0063] Step S37: Output the multi-section transmission power boundary under the current mode type.

[0064] The above method can generate multi-section coupling non-crossable transmission power condition mapping rules, which can be applied to optimization models such as unit combination and economic dispatch, assisting the dispatching department to explore the potential of transmission channels and facilitate the transmission and consumption of new energy.

[0065] Anyone skilled in the art can, without departing from the scope of the technical solution of the present invention, make many possible changes and modifications to the technical solution of the present invention using the above technical content, or modify it into equivalent embodiments with equivalent changes. Therefore, any changes, modifications, equivalent changes, and modifications made to the above embodiments based on the technology of the present invention that do not depart from the content of the technical solution of the present invention are within the scope of protection of the technical solution.

Claims

1. A data-driven multi-level accurate characterization method for ensuring that cross-sections cannot cross the transmission power boundary, characterized by: The method comprises the following steps: Step S1: Using a clustering algorithm based on a Gaussian mixture model to perform unsupervised learning on the grid operation mode data to generate operation mode sub-mode clusters; Step S2: in each sub-pattern cluster, calculate the initial boundary of a single section according to the conservative principle; Step S3: Use the Alpha Shape algorithm to search for the boundary of the instability region, construct the coupling boundary, and calculate the union with the initial boundary to form the final uncrossable transmission power boundary constraint; The clustering algorithm of Gaussian mixture model is used to decompose the operation mode sample space into several models based on Gaussian probability density function, including components The Gaussian mixture model is shown below: （1） in, for Gaussian probability density function; represents the mean vector; It is the operation mode collection; yes -dimensional covariance matrix; is the probability density function of the Gaussian mixture model; is the mixing weight, which represents the The weight coefficient of a single Gaussian function in GMM; is a sample vector set of operation modes, where the vector Including active output of traditional units , Active power output of new energy units , load active and DC transmission ; The initial boundary calculation of a single section in each operating mode cluster is as follows: （5） in, For the expected accident set; A collection of clusters of different modes of operation; For the A cluster of operating mode sub-modes; For the The working condition A safety label after the safety and stability verification of a predicted accident, 0 means unsafe, and 1 means the opposite; For the Section transmission power under each working condition; , Respectively The minimum active power flow of the section in the unstable operation mode and the maximum active power flow of the section in the stable operation mode in each operation mode sub-mode cluster; The specific steps of step S3 include: Step S31: Input cross-sectional power sample data: , boundary adhesion control parameters: ; Step S32: Construct Delaunay triangulation and calculate power sample data Delaunay triangulation of the generated set of triangles and their edges, is the set of all triangles in the triangulation; ； in, Indicates power sample data The convex hull of Step S33, calculate the empty sphere radius of all Delaunay edges, for each edge , calculate the circumcircle radius of each triangle , take the smallest As the radius of the empty sphere; Step S34: For each edge , if the radius of the empty sphere is , then retain ; Otherwise delete; Step S35: Connect all the retained edges to form the boundary of the Alpha Shape. The remaining boundary points constitute the final boundary polygon, which is recorded as ; Step S36, the initial boundary generated by formula (5) Find the union to form the transmission power boundary constraint that cannot be crossed: , Run Mode Cluster Moderately unstable operating mode set; Indicates approximation Conservative non-transgressable transmission power bounds of the set true bounds; Step S37: Output the multi-section transmission power boundary under the current mode type. .

2. The data-driven multi-level accurate characterization method for cross-section transmission power boundary according to claim 1, characterized in that: When performing cluster analysis, the maximum likelihood function is used for parameter estimation: （2） in, is the mixing weight, is the likelihood function, and the maximum likelihood function is used to find Parameters that reach their maximum value , , Finally, we get the cluster of operation mode sub-modes 。 3. The data-driven multi-level accurate characterization method for cross-section transmission power boundary according to claim 2 is characterized by: When estimating parameters, we use The algorithm is calculated, the specific method is: According to the specified 、 and Initial value, calculate the probability that each data point belongs to different categories, data point Belong to category The posterior probability is: （3） According to the obtained posterior probability results, the maximum likelihood method is used to obtain the new 、 and , the calculation formula is as follows: （4） Repeatedly calculate the posterior probability and the new 、 and , until the log-likelihood function meets the convergence condition , and get the Gaussian mixture model parameter values.

Images