Island partitioning method for high-proportion new energy power grid considering frequency constraint

Abstract

The application discloses a high-proportion new energy power grid island division method considering frequency constraints and belongs to the technical field of power system stability analysis and control, comprising the following steps: calculating the coherent coupling matrix of generators and new energy stations by using point voltage phase angle information; constructing a coherent information undirected graph and calculating a normalized Laplace matrix; performing eigenvalue analysis to determine the number of coherent machine groups and the coordinates of the generators and the new energy stations; determining coherent machine group composition through inverse mapping to obtain multi-type power source grouping results; establishing coherent grouping constraints and frequency safety constraints according to the multi-type power source grouping results; constructing an island division optimal section search model and solving the model to obtain an optimal solution section. The application adopts the above method, realizes coherent grouping of multi-type power sources, constructs an island division optimal section search model considering new energy support capacity and frequency constraints and solves the model, and thus an optimal island division scheme is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system stability analysis and control technology, in particular to a high-proportion new energy power grid island division method considering frequency constraints. BACKGROUND

[0002] With the continuous expansion of high-proportion new energy grid connection and regional grid interconnection, the operation mode of power grid is complex and changeable, and its safety and stability is facing new challenges. In the event of extreme situations such as power grid disasters, it is more likely to cause the expansion of local accidents, causing huge losses to society and economy. The island division after the active splitting of the power system is the last line of defense to avoid the collapse of the power system, and an unreasonable island division method may lead to a large number of machine and load shedding after splitting, affecting the dynamic stability of the island, and may cause the new energy station to be off-grid, causing a secondary impact on the system.

[0003] The power system multi-type power source grouping is the primary task to achieve island division. At present, the model-based and measurement-based coherent identification method is a common method to achieve multi-type power source grouping. The model-based coherent machine group identification method depends on the detailed model and accurate parameters of the system, making the model-based coherent machine group identification method face great challenges in practical application. On the contrary, the measurement-based method uses wide-area synchronous phasor measurement unit data to identify coherent machine groups. This kind of method uses pattern recognition and data mining related theories to extract power angle information that can represent the coherence between generators from wide-area measured information of the power system to divide coherent machine groups. Determining a reasonable splitting section is the core of island division. At present, the optimization-based method is a common method to search for the optimal splitting section. The core idea of this method is to establish a mathematical programming model to solve the optimal section search problem of active splitting under the condition that the generator grouping result is known. However, in the practical application of high-proportion new energy power grid, the above island division methods have the following shortcomings:

[0004] ①The coherent mechanism of current new energy stations has not been clarified, and the traditional coherent grouping method is difficult to apply to high-proportion new energy power grid. The research on coherent grouping of multi-type power sources still needs to be further deepened; ②The support capacity of new energy stations is not taken into account, and the traditional splitting section search method cannot meet the needs of island division of high-proportion new energy power grid; ③Most of the current island division methods focus on the solution algorithm of the optimal splitting section problem and ignore other stability constraints in the power grid.

[0005] Therefore, it is of great significance to study how to propose an island division method suitable for high-proportion new energy power grid considering frequency safety constraints according to the actual needs of high-proportion new energy power grid. SUMMARY

[0006] The purpose of this invention is to provide a method for islanding a high proportion of renewable energy power grids that takes into account frequency constraints. It uses node voltage information to achieve coherence grouping of multiple types of power sources. Based on considering the support capacity of renewable energy and frequency constraints, an optimal cross-section search model for islanding is constructed. By solving the optimal cross-section search model for islanding, the optimal islanding scheme is obtained.

[0007] To achieve the above objectives, this invention provides a method for islanding high-proportion renewable energy power grids that takes frequency constraints into account, comprising the following steps:

[0008] S1. Based on the wide-area measurement device, collect the node voltage phase angle information of generators and new energy power stations in the power system and calculate the frequency deviation value. Calculate the cosine similarity between each power node based on the frequency deviation value to obtain the coherence coupling degree matrix of generators and new energy power stations in each power system in the high-proportion new energy power grid.

[0009] S2. Based on the obtained coherence coupling degree matrix of generators and new energy power stations, construct the coherence information undirected graph of high proportion of new energy power grid, calculate the weight matrix of the coherence information undirected graph, and construct the normalized Laplace matrix of the coherence information undirected graph.

[0010] S3. Perform eigenvalue analysis on the normalized Laplace matrix, calculate its eigenvalues ​​and eigenvectors, determine the number of co-located generator groups in the power system based on the eigenvalues, and obtain the coordinate distribution of generators and new energy power stations in Euclidean space based on the eigenvectors.

[0011] S4. Determine the composition of the coordinating generator group through cluster analysis and inverse spatial coordinate mapping, merge the coordinating generator groups according to the actual power grid operation scale limitations, and determine the final multi-type power source grouping results.

[0012] S5. Establish homogeneity grouping constraints and frequency security constraints based on the results of multi-type power supply grouping.

[0013] S6. Based on homology grouping constraints and frequency constraints, construct an optimal cross-section search model for island partitioning, solve the optimal cross-section search model for island partitioning, obtain the optimal solution cross-section, and obtain the island partitioning result.

[0014] Preferably, step S1 specifically includes:

[0015] An extended dynamic coherence identification method is used to describe the generator-like coherence characteristics exhibited by renewable energy power plants in a power system after being disturbed. The frequency deviation between the generator and the renewable energy power plant at a certain moment in the power system is calculated using the voltage phase angle change rate, as shown in the formula:

[0016]

[0017] In the formula, Δf i| t This indicates the frequency deviation between the generator and the new energy power station. Let ω be the voltage phase angle at node i. o Δt represents the rated angular frequency, Δt represents the time interval, and t represents a specific moment.

[0018] Calculate the frequency deviation vector Δf between generators and new energy power stations over a certain time period. i , Δf i Constructed from the frequency deviation values ​​at different times, the formula is:

[0019]

[0020] In the formula, N represents the number of generators and new energy power station nodes;

[0021] Based on the difference in frequency deviation vectors between generators and new energy power station nodes, the cosine similarity between each power node is calculated, thereby determining the synchronized generator group. The formula is as follows:

[0022]

[0023] In the formula, CC ij Represents cosine similarity, CS ij This indicates the coherence coupling degree between the power supplies at node i and node j;

[0024] The coherence coupling degree of each generator and the new energy power station is calculated based on the cosine similarity, resulting in the coherence coupling degree matrix C of the system's generators. The formula is as follows:

[0025]

[0026] Preferably, in step S2, the undirected graph of the high proportion of new energy power grid is G = (V, E), where V represents the set of vertices of G, corresponding to the set of generators and new energy power stations in the power system; and E represents the set of edges of G, corresponding to the set of coherence coupling degrees between generators and new energy power stations.

[0027] Preferably, step S2, which involves calculating the weight matrix of the homology information undirected graph and constructing the normalized Laplacian matrix of the homology information undirected graph, includes:

[0028] Based on a homology-information undirected graph G, the vertex weights and edge weights of G are defined as follows:

[0029] w ii =CC ii =1;

[0030] w ij =CS ij ;

[0031] In the formula, wii w represents the vertex weight. ij Indicates edge weight;

[0032] The weight matrix of the undirected graph G with homology information is obtained based on vertex weights and edge weights;

[0033] The non-normalized Laplacian matrix L is constructed from the weight matrix of the undirected graph G based on homology information. The construction process includes:

[0034]

[0035] In the formula, L ij d represents an element in L. i d represents the weight factor of vertex i in the undirected graph G containing homology information. i The expression is:

[0036]

[0037] Combining the weight factor of vertex i, the normalized Laplace matrix can be further expressed as:

[0038]

[0039] In the formula, D is the vertex weight factor d i The resulting diagonal matrix.

[0040] Preferably, step S3 includes:

[0041] For the normalized Laplace matrix L N Perform eigenvalue analysis, calculate its eigenvalues ​​and eigenvectors, and then apply the normalized Laplace matrix L. N The maximum characteristic gap is used to determine the number of coherent units in the system, as shown in the formula:

[0042] Δλ k =λ k -λ k-1 ;

[0043] In the formula, k is the normalized Laplace matrix L N Maximum characteristic gap Δλ max The corresponding value represents the number of synchronized machine groups;

[0044] Based on the number of coherent machine groups k, the normalized Laplace matrix L N The first k eigenvectors u1, u2, ..., u k The elements are assigned row by row to the elements in the vertex set V of the homogeneous information undirected graph G, thus obtaining the coordinate information of each generator and new energy station in the vertex set V in the k-dimensional Euclidean space.

[0045] Preferably, step S5, which establishes homogeneity grouping constraints and frequency security constraints based on the multi-type power supply grouping results, includes:

[0046] Based on the grouping of the synchronously operating units, the power system is split into N groups. A For each isolated island, a grouping constraint is constructed based on the islands, and its expression is:

[0047]

[0048] In the formula, x i,k This represents the 0-1 variable partitioned by node i. If x i,k =1, then node i belongs to a point inside island k; otherwise, x i,k =0, node i does not belong to island k, x j,k This represents the 0-1 partitioning of node j. If x j,k =1, then node j belongs to a point inside island k; otherwise, x j,k =0, node j does not belong to island k, i and j represent the nodes at both ends of line l, E represents the set of lines, U ij Represents the line partitioning 0-1 variable, representing the connectivity state of branch (i,j). If U ij =0 indicates that branch (i,j) is disconnected through unblocking; otherwise, U ij =1, branch is connected; z ij,k Indicates auxiliary 0-1 variables;

[0049] Considering that the minimum and maximum frequencies are related to the power system inertia and generator governor response, frequency constraints are constructed to ensure that the power system has sufficient inertia and primary frequency response reserves after active disconnection to maintain the dynamic stability of the islanded subsystem frequency. The expression for this constraint is:

[0050]

[0051] In the formula, These represent the upper reserve of the generator's primary frequency response when a power deficit occurs and the lower reserve of the generator's primary frequency response when a power surplus occurs, respectively. These represent the upper reserve of the primary frequency response of the renewable energy power station when a power deficit occurs and the lower reserve of the primary frequency response of the renewable energy power station when a power surplus occurs, respectively. This indicates the lowest frequency point at which a power deficit occurs; This indicates the highest frequency point where power surplus occurs; c i Indicates the power regulation rate of generators or new energy power plants; H * k Let fk represent the equivalent inertia of island k, and f0 represent the rated frequency of the power system. These represent the power surplus and deficit, respectively; f DBThe dead zone frequency is represented by Ω, w represents the node of the new energy power station, and Ω represents the dead zone frequency. k This represents the set of generators and new energy power stations on island k.

[0052] To ensure that the rate of change of the frequency of the isolated subsystem does not exceed its limit after de-isolating, the surplus or deficit within the island is limited, as shown in the formula:

[0053]

[0054] In the formula, RoCoF max This indicates the maximum permissible rate of frequency variation for power grid operation.

[0055] Preferably, in step S6, the optimal cross-section search model for island partitioning is constructed based on homology constraints and frequency constraints, including:

[0056] An objective function is established for the optimal cross-section search model of power system islanding. The objective function aims to minimize the total load shedding by generators and the cost of disconnecting lines. The expression is as follows:

[0057] min∑ l∈E (1-U ij )λ ij +∑ i∈D ΔP Di λ d ;

[0058] In the formula: λ ij λ represents the cost of opening a path. d Indicates the load shedding penalty coefficient; ΔP Di For the load shedding of isolated node i;

[0059] Considering the active and reactive power balance equations for load shedding and power generation changes at each node, as well as the changes in active and reactive power output of generators and renewable energy plants and the range of load shedding, node power balance constraints are established, and their expressions are as follows:

[0060]

[0061] In the formula, P Gi Q Gi P represents the active and reactive power output of the generator during normal operation. Wi This indicates the power output of the new energy power station during normal operation; P l Q l P represents the active and reactive power of branch l, respectively; Di Q Di Q represents the active and reactive loads of node i, respectively; c Q represents the reactive power dispatch value of capacitor bank c; s This represents the scheduling value of the static var compensator s; ΔP Gi ΔQGi ΔP represents the changes in active and reactive power output of the generator, respectively. Wi E represents the change in the scheduling of new energy power stations; Ri E Oi These represent the receiving-end bus and the sending-end bus of the transmission line, respectively; ΔP Gmax ΔQ Gmax P represents the maximum value of the changes in active and reactive power of the generator; Dmax Indicates the maximum load that can be removed; ΔP Wmax This represents the maximum adjustable range of the new energy power station; the line power flow constraint is established, and its expression is:

[0062]

[0063] In the formula, M represents an arbitrarily large number. U represents an auxiliary variable. ij P is the line switching variable. ij G represents the active power flowing through branch (i,j). ij B represents the conductance of branch (i,j). ij V represents the susceptance of the conductance of path (i,j). i V j δ represents the voltage magnitude at node i and node j, respectively. i and δ j Let i and j represent the voltage phase angles at nodes i and j, respectively.

[0064] Connectivity constraints are established so that after active disconnection of the power system, the resulting islands are internally connected but not interconnected, and each node can belong to only one island. The expression for this constraint is:

[0065]

[0066] In the formula: P l ' represents the active power of the virtual branch; P r ' ef This represents the active power output of the virtual generator, and its value is greater than or equal to 1 to ensure that there are no isolated generator nodes in the island.

[0067] Establish unbalanced power constraints within the island, where unbalanced power is represented by power surplus or deficit, expressed as follows:

[0068]

[0069]

[0070] In the formula, P Gi P Wi P DiThese represent the output power of the generators, the new energy power stations, and the load power in island k, respectively. δ represents the magnitude of unbalanced power in island k, and is a binary variable representing the relationship between the power surplus and deficit in the island. The two cannot coexist in an island.

[0071] Preferably, in step S6, the solver Cplex is used to solve the island partitioning optimal cross-section search model to obtain the optimal solution cross-section and thus the island partitioning result.

[0072] Therefore, the above-mentioned method for islanding high-proportion renewable energy power grids that takes frequency constraints into account has the following beneficial effects:

[0073] (1) This invention accurately and effectively evaluates the co-homology characteristics of generators and new energy power plants by using node voltage phase angle information, and realizes co-homology grouping of multiple types of power sources.

[0074] (2) This invention considers the influence of the virtual inertia and power support of new energy power stations on the optimal cross-section search, ensuring the accuracy of the optimal cross-section search results for island division;

[0075] (3) The islanding method of the present invention takes into account frequency security constraints and new energy support capabilities, and can be applied to actual high-proportion new energy power grids. The islanded power grids after the division have sufficient frequency support capabilities to ensure the safe and stable operation of high-proportion new energy power grids.

[0076] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0077] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram of the primary frequency response mode of a high-proportion renewable energy power grid according to an embodiment of the present invention;

[0079] Figure 3 This is a modified IEEE 39-node system topology diagram according to an embodiment of the present invention;

[0080] Figure 4 This is a node voltage phase angle diagram according to an embodiment of the present invention;

[0081] Figure 5 This is an eigenvalue diagram of the normalized Laplace matrix according to an embodiment of the present invention;

[0082] Figure 6 This is a gap diagram of the eigenvalues ​​of the normalized Laplacian matrix according to an embodiment of the present invention;

[0083] Figure 7This is a three-dimensional spatial coordinate diagram of the generator and wind farm in an embodiment of the present invention.

[0084] Figure 8 This is a schematic diagram of island partitioning without considering frequency security constraints in an embodiment of the present invention.

[0085] Figure 9 This is a schematic diagram of islanding for an embodiment of the present invention, considering frequency security and stability constraints and the participation of new energy sources in regulation. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0087] Example

[0088] Reference Figure 1 This invention provides a method for islanding high-proportion renewable energy power grids that takes frequency constraints into account, the steps of which include:

[0089] S1. Based on a wide-area measurement device, collect node voltage phase angle information of generators and new energy power plants in the power system and calculate the frequency deviation value Δf. i | t The cosine similarity CC between each power supply node is calculated based on the frequency deviation value. ij This yields the coherence coupling degree matrix C of generators and renewable energy power plants in a high-proportion renewable energy power grid. Specifically, it includes:

[0090] The frequency deviation phasor of a traditional generator can be represented by equation (1), which is:

[0091]

[0092] In the formula, δ represents the generator power angle, f0 is the rated frequency, and ω0 is the rated angular frequency.

[0093] An extended dynamic coherence identification method is used to describe the coherence characteristics of renewable energy power plants in a power system after being disturbed, similar to those of traditional generators. Specifically, node voltage phase angle information is used to replace the generator power angle. The frequency deviation between the generator and the renewable energy power plant at a given moment in the power system can be calculated using the voltage phase angle change rate, as shown in the formula:

[0094]

[0095] In the formula, Δf i | t This indicates the frequency deviation between the generator and the new energy power station. Let ω be the voltage phase angle at node i. o Δt represents the rated angular frequency, Δt represents the time interval, and t represents a specific moment.

[0096] Calculate the frequency deviation vector Δf between generators and new energy power stations over a certain time period. i , Δf i Constructed from the frequency deviation values ​​at different times, the formula is:

[0097]

[0098] In the formula, N represents the number of generators and new energy power station nodes in the power system.

[0099] Since there are differences in the frequency deviation vectors between generators and renewable energy power station nodes, cosine similarity is used as an index of the coherence coupling degree between generators and renewable energy power stations to determine the coherent generator group. The formula is as follows:

[0100]

[0101] In the formula, CS ij This represents the coherence coupling degree between node i and node j.

[0102] The coherence coupling degree of each generator and new energy power station is calculated based on the cosine similarity equations (4) and (5), and the coherence coupling degree matrix C of the system generators is obtained, with the formula as follows:

[0103]

[0104] S2. Based on the obtained coherence coupling degree matrix C of generators and new energy power plants, construct an undirected graph G of coherence information for a high-proportion new energy power grid, calculate the weight matrix w of the undirected graph, and construct the normalized Laplace matrix L of the undirected graph. N Specifically, this includes:

[0105] A homogeneous undirected graph G = (V, E) is constructed using the homogeneous coupling degree between each generator and new energy power station. V represents the set of vertices of G, corresponding to the set of generators and new energy power stations in the power system; E represents the set of edges of G, corresponding to the set of homogeneous coupling degrees between generators and new energy power stations.

[0106] Based on the definition of a homology-information undirected graph G, the vertex weights and edge weights of the homology-information undirected graph G are defined as follows:

[0107] w ii =CC ii =1 (7)

[0108] w ij =CS ij (8)

[0109] In the formula, w ii w represents the vertex weight. ij The edge weight is represented by ; the weight matrix w of the undirected graph G with coherent information is obtained based on the vertex weight and edge weight.

[0110] The normalized Laplacian matrix L is constructed based on the weight matrix of the homology information undirected graph G to achieve graph partitioning of the homology information undirected graph G. The construction process is as follows:

[0111]

[0112] In the formula, L ij d represents an element in L. i d represents the weight factor of vertex i in the undirected graph G containing homology information. i The expression is:

[0113]

[0114] Based on the non-normalized Laplacian matrix L constructed according to equation (9), and combined with the weight factor of vertex i, the normalized Laplacian matrix L of the homology information undirected graph G is further constructed. N Expressed as:

[0115]

[0116] In the formula, D is the vertex weight factor d i The resulting diagonal matrix.

[0117] S3, regarding the normalized Laplace matrix L N Eigenvalue analysis is performed to calculate eigenvalues ​​and eigenvectors. The number of synchronized generator groups k in the power system is determined based on the eigenvalues, and the coordinate distribution of generators and new energy power plants in k-dimensional Euclidean space is obtained based on the eigenvectors.

[0118] Specifically, it includes:

[0119] For the normalized Laplace matrix L N Perform eigenvalue analysis, calculate its eigenvalues ​​and eigenvectors, and then apply the normalized Laplace matrix L. N The maximum characteristic gap is used to determine the number of coherent machines in the system, using the following formula:

[0120] Δλ k =λ k -λ k-1 (12)

[0121] In the formula, k is the normalized Laplace matrix L N Maximum characteristic gap Δλ max The corresponding value represents the number of synchronized machine groups;

[0122] Based on the number of coherent machine groups k, the normalized Laplace matrix L N The first k eigenvectors u1, u2, ..., u k The elements are assigned row-wise to the elements in the vertex set V of the homology information undirected graph G, thus obtaining the coordinate information of each generator and new energy station in the vertex set V in k-dimensional Euclidean space, i.e. (u 1i ,u 2i ,···,u ki ).

[0123] S4. Determine the composition of k coordinating generator groups through cluster analysis and inverse spatial coordinate mapping. Merge the coordinating generator groups according to the actual power grid operation scale limitations to determine the final multi-type power source grouping results.

[0124] Specifically, in k-dimensional space, a clustering algorithm is used to cluster generators and renewable energy power plants in the vertex set V into k classes, achieving graph partitioning of the undirected graph G of coherent information. Based on the actual grid operation scale constraints, coherent generator groups are merged to determine the final multi-type power source grouping result N. A .

[0125] S5. Establish homogeneity grouping constraints and frequency security constraints based on the grouping results of multiple power sources. Specifically:

[0126] Homogeneity grouping constraints

[0127] Based on the grouping of the synchronously operating units, the power system is split into N groups. A For each isolated island, a grouping constraint is constructed based on the islands, and its expression is:

[0128]

[0129] Equation (13) indicates that each node can only belong to one island. Equation (14) determines whether nodes i and j belong to the same island, thereby deciding whether the branch is open or closed. Since it is the product of two binary variables, Equation (15) introduces an auxiliary variable z. l,k After linearization, a linear expression is finally obtained. i,k This represents the 0-1 variable partitioned by node i. If x i,k =1, then node i belongs to a point inside island k; otherwise, x i,k =0, node i does not belong to island k, x j,k This represents the 0-1 partitioning of node j. If x j,k =1, then node j belongs to a point inside island k; otherwise, x j,k =0, node j does not belong to island k, i and j represent the nodes at both ends of line l, l represents the line, E represents the set of lines, U ij Represents the line partitioning 0-1 variable, representing the connectivity state of branch (i,j). If U ij =0 indicates that branch (i,j) is disconnected through unblocking; otherwise, U ij =1, branch is connected; z ij,k This represents an auxiliary 0-1 variable.

[0130] Frequency security constraints

[0131] The generator rotor motion equation considering the virtual inertia and power support effect of new energy sources is shown in equation (16):

[0132]

[0133] In the formula: f(t) is the system frequency; df(t) / dt is the rate of change of frequency; H * P is the system's equivalent inertia. m (t), P w (t), P e (t) represents the system's mechanical power, renewable energy power, and electrical load, respectively.

[0134] like Figure 2 The figure shows a schematic diagram of the primary frequency response model of a high-proportion renewable energy power grid. From the figure, it can be seen that P... m (t)+P w (t)-P e (t), based on this formula, equation (16) in 0-t nadir Integrate over the interval t nadir Representing the moment of lowest frequency, we can obtain:

[0135]

[0136] Equation (17) is a way to find the lowest frequency point fnadir With system rated frequency f0, power deficit P l System speed controller dead time t db And the algebraic expression relating this to the system's ramp rate C, from which the minimum ramp rate of the power system can be obtained:

[0137]

[0138] Because the speed controller has a dead zone f db In the initial moment of power shortage, the system frequency is driven solely by the system's inertial response; therefore, the dead time t... db and governor dead zone f db The following relationship exists:

[0139]

[0140] Substituting equation (19) into equation (18), we obtain the primary frequency response constraint for a single generator or new energy power station as follows:

[0141]

[0142] To ensure that the system has sufficient inertia and backup frequency response after active disconnection to maintain dynamic frequency stability, the relevant constraints on frequency stability are modeled based on the above derivation conclusions.

[0143] Considering that the minimum and maximum frequencies are related to the power system inertia and the generator governor response, based on the previous derivations (20) and (21), the sufficient conditions for satisfying the primary frequency response criterion after a fault are obtained, and frequency constraints are constructed, the expression of which is:

[0144]

[0145] In the formulas, equations (22) and (23) ensure that the primary frequency response reserve of each generator or new energy power station can be provided when or before the frequency minimum or maximum point occurs; equations (24) and (25) require that the primary frequency response reserve capacity of the co-tuning group should completely cover the remaining surplus or deficit in the island after decoupling. These represent the upper reserve of the generator's primary frequency response when a power deficit occurs and the lower reserve of the generator's primary frequency response when a power surplus occurs, respectively. These represent the upper reserve of the primary frequency response of the renewable energy power station when a power deficit occurs and the lower reserve of the primary frequency response of the renewable energy power station when a power surplus occurs, respectively. This indicates the lowest frequency point at which a power deficit occurs; This indicates the highest frequency point where power surplus occurs; c i For the power regulation rate of generators or new energy power plants; H* k Let f0 be the equivalent inertia of island k, and f0 represent the rated frequency of the power system. These represent the power surplus and deficit, respectively; f DB The dead zone frequency is represented by Ω, w represents the node of the new energy power station, and Ω represents the dead zone frequency. k This represents the set of generators and new energy power stations on island k.

[0146] After a disturbance of power deficit occurs, the rate of change of the system frequency is directly proportional to the actual deficit and inversely proportional to the equivalent inertia of the system. To ensure that the rate of change of the frequency of the isolated subsystem after decoupling does not exceed its limit, the surplus or deficit within the island is limited according to equations (26) and (27), as shown below:

[0147]

[0148] In the formula, RoCoF max This indicates the maximum permissible rate of frequency change limit for power grid operation.

[0149] S6. Based on homology grouping constraints and frequency constraints, construct an optimal cross-section search model for island partitioning, solve the optimal cross-section search model to obtain the optimal solution, and obtain the island partitioning result. Specifically, this includes:

[0150] An objective function is established for the optimal cross-section search model of power system islanding. The objective function aims to minimize the sum of load shedding and line disconnection costs, and its expression is:

[0151] min∑ l∈E (1-U ij )λ ij +∑ i∈D ΔP Di λ d (28)

[0152] In the formula: λ ij λ represents the cost of opening a path. d Indicates the load shedding penalty coefficient; ΔP Di The load is the load of the isolated node i.

[0153] Node power balance constraints

[0154] Considering the active and reactive power balance equations for load shedding and power generation changes at each node, as well as the changes in active and reactive power output of generators and renewable energy plants and the range of load shedding, node power balance constraints are established, and their expressions are as follows:

[0155]

[0156] In the formula, P Gi Q GiP represents the active and reactive power output of the generator during normal operation. Wi This indicates the power output of the new energy power station during normal operation; P l Q l P represents the active and reactive power of branch l, respectively; Di Q Di Q represents the active and reactive loads of node i, respectively; c Q represents the reactive power dispatch value of capacitor bank c; s This represents the scheduling value of the static var compensator s; ΔP Gi ΔQ Gi ΔP represents the changes in active and reactive power output of the generator, respectively. Wi E represents the change in the dispatch output of new energy power plants; Ri E Oi These represent the receiving-end bus and the sending-end bus of the transmission line, respectively; ΔP Gmax ΔQ Gmax P represents the maximum value of the changes in active and reactive power of the generator; Dmax Indicates the maximum load that can be removed; ΔP Wmax This indicates the maximum adjustable range of the new energy power station.

[0157] Line power flow constraints

[0158] Establish line power flow constraints, the expression of which is:

[0159]

[0160] In the formula, M represents an arbitrarily large number. U represents an auxiliary variable. ij P is the line switching variable. ij G represents the active power flowing through branch (i,j). ij B represents the conductance of branch (i,j). ij V represents the susceptance of the conductance of path (i,j). i V j δ represents the voltage magnitude at node i and node j, respectively. i and δ j Let represent the voltage phase angles of node i and node j, respectively.

[0161] Connectivity constraints

[0162] Connectivity constraints are established so that after active disconnection of the power system, the resulting islands are internally connected but not interconnected, and each node can only belong to one island. This model can be determined and constructed using the single commodity flow method. The principle and specific method are as follows: First, a virtual assumption is made about the network, assuming that each island contains only one generator node, while all other nodes are load nodes with a per-unit value of 1 pu. If each island satisfies the virtual active power balance constraint, it means that there exists a path from the generator node to all other nodes within the corresponding island, thus ensuring internal connectivity of the island. The expression is:

[0163]

[0164] In the formula, P l ' represents the active power of the virtual branch; P r ' ef This represents the active power output of the virtual generator, and its value is greater than or equal to 1 to ensure that there are no isolated generator nodes in the island.

[0165] Unbalanced power constraints within islands

[0166] An unbalanced power constraint is established within an island. The unbalanced power within the island is represented by a power surplus or a power deficit. The power surplus represents the portion of the power generation from generators and renewable energy sources within the island that exceeds the load, while the power deficit represents the portion of the power generation from generators and renewable energy sources within the island that is less than the load. Equation (35) represents the unbalanced power within the island, and Equation (36) ensures that a surplus and a deficit cannot exist simultaneously within an island. The expression is as follows:

[0167]

[0168] In the formula, P Gi P Wi P Di These represent the output power of the generators, the new energy power stations, and the load power in island k, respectively. δ represents the magnitude of unbalanced power in island k, and is a binary variable representing the relationship between the power surplus and deficit in the island. The two cannot coexist in an island.

[0169] Finally, based on the homology grouping constraint, frequency constraint, and other constraints of power system operation, the Cplex solver is used to solve the island partitioning optimal section search model to obtain the optimal solution section and the island partitioning result.

[0170] The method of the present invention will be verified below with specific examples. A simulation analysis and verification will be performed using the modified IEEE-39 node system as an example. The topology diagram of the modified IEEE-39 node system is shown below. Figure 3 As shown

[0171] The modified IEEE 39-node system topology diagram is as follows: Figure 3 As shown, the simulation includes 6 generator sets, 4 new energy power stations, and 46 branch lines. Taking a wind farm as an example, the generators at nodes 32, 34, 35, and 37 are replaced with wind farms of equal capacity. Using generator G2 as the reference generator, a scenario is simulated that causes the system to collapse after a disturbance: at 0s, a three-phase permanent fault is introduced on an AC branch between nodes 16 and 17 near node 17. The fault lasts for 0.3s, after which the faulty line is disconnected. The entire simulation lasts for 5s. During this period, the relative movement trend of the bus voltage phase angle is shown in the figure. Figure 4 As shown.

[0172] by Figure 4 The voltage phase angle with a time window of 0.3 to 5 s is used as the input of the method proposed in this invention. First, the input signal is standardized; then, the coherence coupling degree matrix C of the generator and the wind farm is calculated by equations (4) and (5); based on the calculated coherence coupling degree matrix C, the weight matrix w of the undirected graph G of coherence information is constructed according to equations (7) and (8); based on the obtained weight matrix w, the nonnormalized Laplace matrix L of the undirected graph G of coherence information is constructed according to equation (9); based on the obtained nonnormalized Laplace matrix L, the normalized Laplace matrix L of the undirected graph G of coherence information is further calculated by equation (11). N Then, eigenvalue analysis was performed, and the eigenvalue results are as follows: Figure 5 As shown, the eigenvalue gap results are as follows: Figure 6 As shown. The normalized Laplacian matrix L is calculated according to the method proposed in step S3. N The maximum eigenvalue gap is used to determine the number of coherent machine groups. Clearly, this is determined by... Figure 6 It can be known that: L N The maximum characteristic gap is Δλ3, therefore, the optimal number of coherent machines k in the system is 3.

[0173] Based on the determined optimal number of synchronized machine groups 3 and L N The first three corresponding eigenvectors, in 3D Euclidean space, determine the geometric coordinates of the generator and wind farm, as shown in the following figure. Figure 7 As shown in the figure. Further, based on the calculated spatial distribution of each generator, the generators and wind farms were clustered, with a cluster size of 3, resulting in three co-tuning generator groups, as shown in Table 1. These are: Co-tuning generator group 1, composed of generators G4, G7, and G9 and wind farm stations G5 and G6; Co-tuning generator group 2, composed of generator G1 and wind farm stations G3 and G8; and Co-tuning generator group 3, composed of generator G10. Clearly, this result is consistent with... Figure 4The observed voltage phase angle changes of generators and new energy power stations under fault conditions are consistent, verifying the correctness and effectiveness of the multi-type power source grouping method proposed in the embodiment.

[0174] Table 1. Results of Coherent Machine Group Identification

[0175] Homologous machine group Machine group 1 G4, G5, G6, G7, G9 2 G1, G3, G8 3 G10

[0176] Based on the coherence identification results, Coherence Cluster 3 has only one generator. Due to the limitations of the power system scale, dividing it into an islanded subsystem makes it difficult to maintain stable operation. Time-domain simulation... Figure 4 As can be seen, the voltage phase angle variation pattern of node G10 is similar to that of co-tuning generator group 2. Therefore, co-tuning generator group 2 and co-tuning generator group 3 are merged, ultimately dividing the generators and wind farms into two groups: {G1—G3, G8—G10} and {G4—G7, G9}. Further, based on the division results of generators and new energy power plants, an optimal solution section search is performed in islanding partitioning. The rated frequency of the power grid is set to 50Hz, the lowest frequency point is set to 49.5Hz, and the governor dead zone f is set to... db =20mHz, and the maximum value of RoCoF is set to 0.8Hz / s. To verify the effectiveness of the proposed optimal solution cross-section search model and to analyze the impact of the first frequency response on the optimal solution cross-section search results, two numerical examples are set up for analysis and simulation.

[0177] Example 1 presents an islanding method without considering frequency security and stability constraints; Example 2 presents an islanding method considering frequency security and stability constraints and involving new energy sources in regulation. The optimization results for the solution sections of Examples 1 and 2 are shown in Table 2, including the solution section, unbalanced power, power generation changes, and load shedding.

[0178] Table 2 Search Results for Separation Sections

[0179]

[0180]

[0181] In Example 1, the power flow impact caused by system disconnection is 419.96MW. Table 2 shows that Island 1's total power generation is 270.40MW less than its total load, making it a power-deficient island. Therefore, excess load needs to be cut to maintain power balance, specifically, 146.65MW and 123.75MW of load need to be cut at BUS-20 and BUS-23 nodes, respectively. Similarly, Island 2's total power generation is 270.40MW more than its total load, making it a power-surplus island. Therefore, generator output needs to be adjusted to maintain power balance, specifically, generators G1 and G10 need to reduce their output by 126.13MW and 144.27MW, respectively. In Example 2, considering the effect of the primary frequency response characteristics of generators and wind farms on system frequency regulation, the unbalanced power of islands 1 and 2 is relatively small under the relevant constraints of system frequency security. The reserves above and below the primary frequency response of each generator and wind farm can balance the power deficit or surplus of the corresponding islands. However, the power flow impact caused by the corresponding system splitting increases to 558.12MW. As shown in Table 2, island 1 is an island where the power generation is greater than the load, with a surplus of 49.6MW. The reserve capacity of wind farm G5 on the island reduces this power surplus. In island 2, after island splitting, there will be an additional 49.6MW of load. The power deficit in the island is supported by the reserve capacity above the primary frequency response of G2 and G4 to reduce the load shedding. Since this invention does not consider transmission line losses, the two islands in Example 1 and Example 2 have the same unbalanced power. Finally, the final island splitting results of Example 1 and Example 2 are as follows: Figure 8 and Figure 9 As shown, the effectiveness of the proposed method for islanding up the proportion of new energy power grids is verified.

[0182] Therefore, the present invention adopts the above-mentioned method for islanding high-proportion renewable energy power grids that takes into account frequency constraints. By considering frequency security constraints and renewable energy support capabilities, an optimal cross-section search model for islanding is constructed, which ensures the accuracy of the search results for the optimal cross-section for islanding.

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for islanding high-proportion renewable energy power grids considering frequency constraints, characterized in that the steps include... include: S1. Based on the wide-area measurement device, collect the node voltage phase angle information of generators and new energy power stations in the power system and calculate the frequency deviation value. Calculate the cosine similarity between each power node based on the frequency deviation value to obtain the coherence coupling degree matrix of generators and new energy power stations in each power system in the high-proportion new energy power grid. S2. Based on the obtained coherence coupling degree matrix of generators and new energy power stations, construct the coherence information undirected graph of high proportion of new energy power grid, calculate the weight matrix of the coherence information undirected graph, and construct the normalized Laplace matrix of the coherence information undirected graph. S3. Perform eigenvalue analysis on the normalized Laplace matrix, calculate its eigenvalues ​​and eigenvectors, determine the number of co-located generator groups in the power system based on the eigenvalues, and obtain the coordinate distribution of generators and new energy power stations in Euclidean space based on the eigenvectors. S4. Determine the composition of the coordinating generator group through cluster analysis and inverse spatial coordinate mapping, merge the coordinating generator groups according to the actual power grid operation scale limitations, and determine the final multi-type power source grouping results. S5. Establish homogeneity grouping constraints and frequency security constraints based on the results of multi-type power supply grouping. S6. Based on homology grouping constraints and frequency constraints, construct an optimal cross-section search model for island partitioning, solve the optimal cross-section search model for island partitioning, obtain the optimal solution cross-section, and obtain the island partitioning result.

2. The method for islanding high-proportion renewable energy power grids considering frequency constraints according to claim 1, characterized in that, Step S1 specifically includes: An extended dynamic coherence identification method is used to describe the generator-like coherence characteristics exhibited by renewable energy power plants in a power system after being disturbed. The frequency deviation between the generator and the renewable energy power plant at a certain moment in the power system is calculated using the voltage phase angle change rate, as shown in the formula: In the formula, Δf i | t This indicates the frequency deviation between the generator and the new energy power station. Let ω be the voltage phase angle at node i. o Δt represents the rated angular frequency, Δt represents the time interval, and t represents a specific moment. Calculate the frequency deviation vector Δf between generators and new energy power stations over a certain time period. i , Δf i Constructed from the frequency deviation values ​​at different times, the formula is: In the formula, N represents the number of generators and new energy power station nodes; Based on the difference in frequency deviation vectors between generators and new energy power station nodes, the cosine similarity between each power node is calculated, thereby determining the synchronized generator group. The formula is as follows: In the formula, CC ij Represents cosine similarity, CS ij This indicates the coherence coupling degree between the power supplies at node i and node j; The coherence coupling degree of each generator and the new energy power station is calculated based on the cosine similarity, resulting in the coherence coupling degree matrix C of the system's generators. The formula is as follows:

3. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 2, characterized in that, In step S2, the undirected graph G = (V, E) represents the set of vertices of G, corresponding to the set of generators and new energy power stations in the power system; E represents the set of edges of G, corresponding to the set of coherence coupling degrees between generators and new energy power stations.

4. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 3, characterized in that, Step S2 involves calculating the weight matrix of the homology information undirected graph and constructing the normalized Laplacian matrix of the homology information undirected graph, including: Based on a homology-information undirected graph G, the vertex weights and edge weights of G are defined as follows: w ii =CC ii =1; w ij =CS ij ; In the formula, w ii w represents the vertex weight. ij Indicates edge weight; The weight matrix of the undirected graph G with homology information is obtained based on vertex weights and edge weights; The non-normalized Laplacian matrix L is constructed from the weight matrix of the undirected graph G based on homology information. The construction process includes: In the formula, L ij d represents an element in L. i d represents the weight factor of vertex i in the undirected graph G containing homology information. i The expression is: Combining the weight factor of vertex i, the normalized Laplace matrix can be further expressed as: In the formula, D is the vertex weight factor d i The resulting diagonal matrix.

5. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 4, characterized in that, Step S3 includes: For the normalized Laplace matrix L N Perform eigenvalue analysis, calculate its eigenvalues ​​and eigenvectors, and then apply the normalized Laplace matrix L. N The maximum characteristic gap is used to determine the number of coherent machines in the system, using the following formula: Dl k =λ k -l k-1 ; In the formula, k is the normalized Laplace matrix L N Maximum characteristic gap Δλ max The corresponding value represents the number of synchronized machine groups; Based on the number of coherent machine groups k, the normalized Laplace matrix L N The first k eigenvectors u1, u2, ..., u k The elements are assigned row by row to the elements in the vertex set V of the homogeneous information undirected graph G, thus obtaining the coordinate information of each generator and new energy station in the vertex set V in the k-dimensional Euclidean space.

6. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 5, characterized in that, Step S5, which establishes coherence grouping constraints and frequency security constraints based on the multi-type power supply grouping results, includes: Based on the grouping of the synchronously operating units, the power system is split into N groups. A For each isolated island, a grouping constraint is constructed based on the islands, and its expression is: In the formula, x i,k This represents the 0-1 variable partitioned by node i. If x i,k =1, then node i belongs to a point inside island k; otherwise, x i,k =0, node i does not belong to island k, x j,k This represents the 0-1 partitioning of node j. If x j,k =1, then node j belongs to a point inside island k; otherwise, x j,k =0, node j does not belong to island k, i and j represent the nodes at both ends of line l, E represents the set of lines, U ij Represents the line partitioning 0-1 variable, representing the connectivity state of branch (i,j). If U ij =0 indicates that branch (i,j) is disconnected through unblocking; otherwise, U ij =1, branch is connected; z ij,k Indicates auxiliary 0-1 variables; Considering that the minimum and maximum frequencies are related to the power system inertia and generator governor response, frequency constraints are constructed to ensure that the power system has sufficient inertia and primary frequency response reserves after active disconnection to maintain the dynamic stability of the islanded subsystem frequency. The expression for this constraint is: In the formula, These represent the upper reserve of the generator's primary frequency response when a power deficit occurs and the lower reserve of the generator's primary frequency response when a power surplus occurs, respectively. These represent the upper reserve of the primary frequency response of the renewable energy power station when a power deficit occurs and the lower reserve of the primary frequency response of the renewable energy power station when a power surplus occurs, respectively. This indicates the lowest frequency point at which a power deficit occurs; This indicates the highest frequency point where power surplus occurs; c i Indicates the power regulation rate of generators or new energy power plants; H * k Let fk represent the equivalent inertia of island k, and f0 represent the rated frequency of the power system. These represent the power surplus and deficit, respectively; f DB The dead zone frequency is represented by Ω, w represents the node of the new energy power station, and Ω represents the dead zone frequency. k This represents the set of generators and new energy power stations on island k. To ensure that the rate of change of the frequency of the isolated subsystem does not exceed its limit after de-isolating, the surplus or deficit within the island is limited, as shown in the formula: In the formula, RoCoF max This indicates the maximum permissible rate of frequency variation for power grid operation.

7. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 6, characterized in that, Step S6 involves constructing an optimal cross-section search model for island partitioning based on homology and frequency constraints, including: An objective function is established for the optimal cross-section search model of power system islanding. The objective function aims to minimize the total load shedding by generators and the cost of disconnecting lines. The expression is as follows: min∑ l∈E (1-U ij )l ij +∑ i∈D ΔP Di l d ; In the formula: λ ij λ represents the cost of opening a path. d Indicates the load shedding penalty coefficient; ΔP Di For the load shedding of isolated node i; Considering the active and reactive power balance equations for load shedding and power generation changes at each node, as well as the changes in active and reactive power output of generators and renewable energy plants and the range of load shedding, node power balance constraints are established, and their expressions are as follows: In the formula, P Gi Q Gi P represents the active and reactive power output of the generator during normal operation. Wi This indicates the power output of the new energy power station during normal operation; P l Q l P represents the active and reactive power of branch l, respectively; Di Q Di Q represents the active and reactive loads of node i, respectively; c Q represents the reactive power dispatch value of capacitor bank c; s This represents the scheduling value of the static var compensator s; ΔP Gi ΔQ Gi ΔP represents the changes in active and reactive power output of the generator, respectively. Wi E represents the change in the scheduling of new energy power stations; Ri E Oi These represent the receiving-end bus and the sending-end bus of the transmission line, respectively; ΔP Gmax ΔQ Gmax P represents the maximum value of the changes in active and reactive power of the generator; Dmax Indicates the maximum load that can be removed; ΔP Wmax This indicates the maximum adjustable range of the new energy power station; Establish line power flow constraints, the expression of which is: In the formula, M represents an arbitrarily large number. U represents an auxiliary variable. ij P is the line switching variable. ij G represents the active power flowing through branch (i,j). ij B represents the conductance of branch (i,j). ij V represents the susceptance of the conductance of path (i,j). i V j δ represents the voltage magnitude at node i and node j, respectively. i and δ j Let i and j represent the voltage phase angles at nodes i and j, respectively. Connectivity constraints are established so that after active disconnection of the power system, the resulting islands are internally connected but not interconnected, and each node can belong to only one island. The expression for this constraint is: In the formula: P′ l P′ represents the active power of the virtual branch. ref This represents the active power output of the virtual generator, and its value is greater than or equal to 1 to ensure that there are no isolated generator nodes in the island. Establish unbalanced power constraints within the island, where unbalanced power is represented by power surplus or deficit, expressed as follows: In the formula, P Gi P Wi P Di These represent the output power of the generators, the new energy power stations, and the load power in island k, respectively. δ represents the magnitude of unbalanced power in island k, and is a binary variable representing the relationship between the power surplus and deficit in the island. The two cannot coexist in an island.

8. The method for islanding a high-proportion renewable energy power grid considering frequency constraints according to claim 7, characterized in that: In step S6, the Cplex solver is used to solve the optimal cross-section search model for island partitioning, obtain the optimal solution cross-section, and obtain the island partitioning result.

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