Energy storage power station collaborative planning method and system based on uncertainty propagation analysis

Abstract

The invention discloses an energy storage power station collaborative planning method and system based on uncertainty propagation analysis. In order to solve the problems that an existing energy storage planning method is indefinite in physical mechanism and insufficient in interpretability, the planning method comprises the steps that operation data of a power system are obtained, and an analysis alternating current probabilistic power flow model used for establishing an analysis relation between system voltage statistical characteristics and line power statistical characteristics is constructed based on the operation data; constructing a propagation matrix representing the uncertainty propagation characteristics of the system based on the analysis of the AC probabilistic power flow model; performing spectral analysis on the propagation matrix to identify one or more dominant propagation modes which play a dominant role in the uncertainty of the system; and based on the one or more dominant propagation modes, determining a planning scheme of at least one type of energy storage power station, the category of the planning scheme including the access position capacity of the energy storage power station. According to the method, energy storage configuration is guided by using an uncertainty physical propagation mechanism, and the risk control effect, the calculation efficiency and the engineering interpretability of a planning scheme are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and more specifically to a collaborative planning method for energy storage power stations based on uncertainty propagation analysis. Background Technology

[0002] As the penetration rate of new energy sources such as wind power and solar power in the power system continues to increase, the randomness and uncertainty of the system are significantly enhanced. Fluctuations in the output of new energy sources not only cause local disturbances at the grid connection point, but also propagate and amplify spatially through the grid topology, ultimately evolving into systemic risks such as power flow exceeding limits on critical lines. Rationally allocating flexible resources such as energy storage power stations is a key means to address this challenge.

[0003] Currently, the planning of energy storage power plants mainly relies on mathematical optimization algorithms, such as modeling the energy storage site selection and capacity determination problem as a large-scale stochastic optimization or robust optimization problem. These methods, under given constraints, aim to minimize investment costs or maximize system benefits to solve for the optimal energy storage configuration. However, these mathematical optimization-based methods have two major limitations in engineering practice:

[0004] First, the physical mechanisms are not explicit, resulting in insufficient interpretability. The optimization model is like a "black box" for planners; while the optimal solution provided by the algorithm is mathematically sound, the underlying physical logic is difficult to understand intuitively. Planners cannot clearly answer the critical engineering question, "Why should energy storage be located in this location?", leading to reduced reliability and maintainability of the solution.

[0005] Secondly, traditional sensitivity analysis has limitations. To aid decision-making, planners often use tools such as power transfer sensitivity. However, traditional sensitivity analysis describes the first-order impact of deterministic power disturbances on the mean line power. In high-uncertainty scenarios, the core issue becomes how fluctuations in nodal power (i.e., variance) propagate and affect line power fluctuations. The propagation mechanisms of second-order statistics (such as variance and covariance) differ from those of first-order means; therefore, decisions based on traditional sensitivity analysis cannot directly and effectively suppress system uncertainty.

[0006] Therefore, there is an urgent need for a new method that can reveal the physical mechanism of uncertainty propagation in the power grid, provide clear engineering guidance for energy storage planning, and has high computational efficiency, in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0007] 1. The technical problem to be solved:

[0008] To address the aforementioned technical problems, this invention provides a collaborative planning method and system for energy storage power stations based on uncertainty propagation analysis. The aim is to transform energy storage planning from a "black box optimization" problem into an "interpretable decision" problem based on physical propagation mechanisms, thereby guiding energy storage configuration more accurately and efficiently, suppressing the propagation of uncertainty, and ensuring the safe and stable operation of the power system.

[0009] 2. Technical Solution:

[0010] A collaborative planning method for energy storage power stations based on uncertainty propagation analysis, characterized by: including:

[0011] Step 1: Obtain the operating data of the power system, including the power grid topology, line impedance parameters, renewable energy output, and historical load data.

[0012] Step 2: Based on the operating data, construct an analytical AC probabilistic power flow model for the power system. The analytical AC probabilistic power flow model is used to establish the analytical relationship between the statistical characteristics of system voltage and the statistical characteristics of line power.

[0013] Step 3: Based on the analytical communication probability power flow model, construct a propagation matrix that characterizes the propagation characteristics of uncertainty in the system;

[0014] Step 4: Perform spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a leading role in the uncertainty of the system;

[0015] Step 5: Based on the one or more dominant propagation modes, determine at least one type of planning scheme for energy storage power stations. The categories of the planning scheme include the access location and capacity of the energy storage power stations.

[0016] Further, step one specifically includes: acquiring historical data for a preset sampling period within a preset time period; performing abnormal data preprocessing on the historical data; classifying the preprocessed data into typical operating scenarios using a clustering algorithm; obtaining multiple operating scenarios, each representing a typical system operating condition; and calculating the occurrence frequency of each operating scenario.

[0017] Furthermore, in step two, constructing the analytical AC probabilistic power flow model of the power system specifically includes:

[0018] S21: For each operating scenario, based on historical data samples under that scenario, estimate the real and imaginary part vector V of the bus voltage, as shown in the following formula:

[0019] [ , ] T (1);

[0020] In the above formula, , These are the real and imaginary vectors of the node voltages, respectively; the superscript T indicates the transpose of the matrix.

[0021] S22: Obtain the statistical characteristics of the entire network voltage vector V for this operating scenario, and then obtain its mean vector. Covariance Matrix Verify whether it approximately follows a multivariate Gaussian distribution. ;

[0022] S23: Establish the analytical relationship between line power and voltage state corresponding to this operating scenario; the active power P of line l l Represented as a voltage vector The quadratic form:

[0023] (2);

[0024] Among them, M l is the quadratic power coefficient matrix corresponding to line l, whose elements are uniquely determined by the nodal admittance matrix and the line topology;

[0025] S24: Assume that the real and imaginary parts of the bus voltage vector follow a multivariate Gaussian distribution with a mean μ V The covariance matrix Σ V The expected power E[P] of the line can be derived from the maximum likelihood estimation obtained during normal operation of the power grid. l ], Variance Var(P l and the characteristic function of line l As shown in the following formula:

[0026] (3);

[0027] (4);

[0028] (5);

[0029] In the above formula, tr(.) represents the trace of the matrix; i in the characteristic function represents the imaginary number; j is a number from 1 to n, and n is the total number of nodes included in the line;

[0030] S25: Using the GilPelaez inversion formula, the characteristic function... Numerical integration yields the cumulative distribution function of the line power. Then, the probability α of the line exceeding the limit is calculated. l， As shown in the following formula:

[0031] (6);

[0032] In the above formula, This indicates the rated capacity of line l.

[0033] Furthermore, step three specifically includes:

[0034] S31: As shown in the following formula, the uncertainty index R of this working scenario is defined as the weighted sum of the power variances of all the lines it includes;

[0035] (7);

[0036] In the above formula, L represents the total number of lines included in the work scenario; w l The importance weight of line l is indicated by the above formula; it can be seen from the above formula that the uncertainty index R is a system-level uncertainty index.

[0037] S32: Ignoring the second-order trace term, perform a low-rank decomposition of the voltage covariance matrix as follows, and then define the propagation matrix M in the low-rank space. agg Specifically:

[0038] (8);

[0039] (9);

[0040] In the above formula, Σ inj The injected power covariance is represented by the covariance matrix Σ. V It is calculated; J is the Jacobian matrix.

[0041] Furthermore, step four includes:

[0042] S41: For the propagation matrix M agg Eigenvalue decomposition is performed as follows:

[0043] (10);

[0044] In the above formula, λ k ψ k M respectively agg The eigenvalues ​​and eigenvectors of λ describe the uncertain propagation gain and propagation mode of the system, respectively; k The "amplification intensity" of the k-th propagation mode is measured. A larger eigenvalue indicates a higher degree of amplification of the voltage covariance as it propagates along that mode; the eigenvector Ψ K For the kth propagation mode, the spatial distribution and propagation path of uncertainty among power grid nodes are described;

[0045] S42: Based on the magnitude of the eigenvalues, determine one or more eigenvectors that contribute the most to the propagation of overall uncertainty in the system as the dominant propagation mode;

[0046] S43: Based on the spatial distribution characteristics of the dominant propagation mode, calculate the mean sensitivity and variance sensitivity of each node respectively; identify the node with high mean sensitivity as the propagation source, the node with high variance sensitivity as the key hub of the propagation channel, and the node with insufficient voltage margin as the weak end.

[0047] Furthermore, in step five, the step of determining at least one type of energy storage power station planning scheme based on the one or more dominant propagation modes is as follows: Pumped storage power stations are configured at propagation source nodes with high mean sensitivity, and the steady-state operating point is reconstructed through intraday energy time shift to adjust the power flow mean field and expand the safety margin of line power; electrochemical energy storage power stations are configured at key hub nodes of propagation channels with high variance sensitivity, and the spectral radius of the propagation matrix is ​​compressed through rapid power response to suppress power variance and reduce the fluctuation amplitude of line power.

[0048] Further, step S43 specifically involves: projecting the dominant propagation mode onto each node of the power grid topology, calculating the mean sensitivity and variance sensitivity respectively, and realizing the quantitative location of weak links and key hub nodes in the power grid;

[0049] Among them, mean sensitivity The following formula is used to evaluate the ability of a node to adjust to the expected value of line power flow:

[0050] (11);

[0051] Variance sensitivity The effect of node compression on the spectral norm of the propagation matrix is ​​defined according to the eigenvalue perturbation theory, as follows:

[0052] (12);

[0053] In the above formula, P i e is the injected power at node i; i Let i be the unit vector corresponding to node i; This represents the dominant mode; K is the feedback gain coefficient for energy storage.

[0054] A collaborative planning system for energy storage power stations based on uncertainty propagation analysis includes:

[0055] The data acquisition module is used to acquire the operating data of the power system, including the power grid topology, line impedance parameters, and historical data on the output and load of new energy sources.

[0056] The probabilistic power flow modeling module is used to construct an analytical AC probabilistic power flow model of the power system based on operational data; the analytical AC probabilistic power flow model is used to establish the analytical relationship between the statistical characteristics of system voltage and the statistical characteristics of line power.

[0057] The propagation characteristics analysis module is used to construct a propagation matrix that characterizes the propagation characteristics of system uncertainty based on the analytical AC probability power flow model, and to perform spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a dominant role in system uncertainty.

[0058] An energy storage planning module is used to determine a planning scheme for at least one type of energy storage power station based on one or more dominant propagation modes. The planning scheme includes the access location and capacity of the energy storage power station.

[0059] 3. Beneficial effects:

[0060] (1) The collaborative planning method for energy storage power stations based on uncertainty propagation analysis provided by this invention has a clear mechanism and strong interpretability: This invention transforms the basis for energy storage planning from an abstract mathematical optimization objective into a clear physical propagation mode. The energy storage site selection and capacity determination scheme is driven by the inherent propagation characteristics of the system, and each decision can be traced back to the corresponding propagation sensitivity. The engineering logic is complete, overcoming the "black box" problem of traditional optimization methods.

[0061] (2) The collaborative planning method for energy storage power stations based on uncertainty propagation analysis provided by this invention can more effectively suppress system risks by directly "blocking" the propagation sources and critical paths of uncertainty. Examples show that, compared with traditional optimization methods, this method can improve risk control effectiveness by more than 20% at similar investment costs.

[0062] (3) The collaborative planning method for energy storage power stations based on uncertainty propagation analysis provided by this invention, based on an analytical model, avoids the large amount of repetitive power flow calculations required by traditional Monte Carlo simulation. For large-scale systems, the calculation time can be shortened from hours to minutes, with a speedup of more than 100 times, which greatly improves the planning efficiency.

[0063] (4) The collaborative planning method for energy storage power stations based on uncertainty propagation analysis provided by this invention reveals the collaborative mechanism: This invention, for the first time from the perspective of mean-variance decoupling, clearly reveals the differentiated role of pumped storage in “reshaping the mean field” and electrochemical energy storage in “suppressing variance”, providing a solid theoretical basis for the scientific collaborative configuration of the two types of energy storage. Attached Figure Description

[0064] Figure 1 This is an overall flowchart of the collaborative planning method for energy storage power stations based on uncertainty propagation analysis of the present invention;

[0065] Figure 2 This is a schematic diagram of the collaborative planning system for energy storage power stations based on uncertainty propagation analysis according to the present invention.

[0066] Figure 3 This is a schematic diagram of the power transmission system in the embodiment;

[0067] Figure 4 This is a diagram showing the proportion of participation factors for each mode of the power grid in the embodiment;

[0068] Figure 5 This is a comparison chart of the mean sensitivity and variance sensitivity of energy storage candidate nodes in the embodiment;

[0069] Figure 6 This is a comparison chart of the eigenvalues ​​and spectral norms of the propagation matrix before and after the energy storage configuration in the example. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings.

[0071] As attached Figure 1 As shown, the collaborative planning method for energy storage power stations based on uncertainty propagation analysis is characterized by including:

[0072] Step 1: Obtain the operating data of the power system, including the power grid topology, line impedance parameters, renewable energy output, and historical load data.

[0073] Step 2: Based on the operating data, construct an analytical AC probabilistic power flow model for the power system. The analytical AC probabilistic power flow model is used to establish the analytical relationship between the statistical characteristics of system voltage and the statistical characteristics of line power.

[0074] Step 3: Based on the analytical communication probability power flow model, construct a propagation matrix that characterizes the propagation characteristics of uncertainty in the system;

[0075] Step 4: Perform spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a leading role in the uncertainty of the system;

[0076] Step 5: Based on the one or more dominant propagation modes, determine at least one type of planning scheme for energy storage power stations. The categories of the planning scheme include the access location and capacity of the energy storage power stations.

[0077] Further, step one specifically includes: acquiring historical data for a preset sampling period within a preset time period; performing abnormal data preprocessing on the historical data; classifying the preprocessed data into typical operating scenarios using a clustering algorithm; obtaining multiple operating scenarios, each representing a typical system operating condition; and calculating the occurrence frequency of each operating scenario.

[0078] Furthermore, in step two, constructing the analytical AC probabilistic power flow model of the power system specifically includes:

[0079] S21: For each operating scenario, based on historical data samples under that scenario, estimate the real and imaginary part vector V of the bus voltage, as shown in the following formula:

[0080] [ , ] T (1);

[0081] In the above formula, , These are the real and imaginary vectors of the node voltages, respectively; the superscript T indicates the transpose of the matrix.

[0082] S22: Obtain the statistical characteristics of the entire network voltage vector V for this operating scenario, and then obtain its mean vector. Covariance Matrix ; Verify whether it approximately follows a multivariate Gaussian distribution ;

[0083] S23: Establish the analytical relationship between line power and voltage state corresponding to this operating scenario; the active power P of line l l Represented as a voltage vector The quadratic form:

[0084] (2);

[0085] Among them, M l is the quadratic power coefficient matrix corresponding to line l, whose elements are uniquely determined by the nodal admittance matrix and the line topology;

[0086] S24: Assume that the real and imaginary parts of the bus voltage vector follow a multivariate Gaussian distribution with a mean μ V The covariance matrix Σ V The expected power E[P] of the line can be derived from the maximum likelihood estimation obtained during normal operation of the power grid. l ], Variance Var(P l and the characteristic function of line l As shown in the following formula:

[0087] (3);

[0088] (4);

[0089] (5);

[0090] In the above formula, tr(.) represents the trace of the matrix; i in the characteristic function represents the imaginary number; j is a number from 1 to n, and n is the total number of nodes included in the line;

[0091] S25: Using the GilPelaez inversion formula, the characteristic function... Numerical integration yields the cumulative distribution function of the line power. Then, the probability α of the line exceeding the limit is calculated. l， As shown in the following formula:

[0092] (6);

[0093] In the above formula, This indicates the rated capacity of line l.

[0094] Furthermore, step three specifically includes:

[0095] S31: As shown in the following formula, the uncertainty index R of this working scenario is defined as the weighted sum of the power variances of all the lines it includes;

[0096] (7);

[0097] In the above formula, L represents the total number of lines included in the work scenario; w l The importance weight of line l is indicated by the above formula; it can be seen from the above formula that the uncertainty index R is a system-level uncertainty index.

[0098] S32: Ignoring the second-order trace term, perform a low-rank decomposition of the voltage covariance matrix as follows, and then define the propagation matrix M in the low-rank space. agg Specifically:

[0099] (8);

[0100] (9);

[0101] In the above formula, Σ inj The injected power covariance is represented by the covariance matrix Σ. V It is calculated; J is the Jacobian matrix.

[0102] Furthermore, step four includes:

[0103] S41: For the propagation matrix M agg Eigenvalue decomposition is performed as follows:

[0104] (10);

[0105] In the above formula, λ k ψ k M respectively agg The eigenvalues ​​and eigenvectors of λ describe the uncertain propagation gain and propagation mode of the system, respectively; kThe "amplification intensity" of the k-th propagation mode is measured. A larger eigenvalue indicates a higher degree of amplification of the voltage covariance as it propagates along that mode; the eigenvector Ψ K For the kth propagation mode, the spatial distribution and propagation path of uncertainty among power grid nodes are described;

[0106] S42: Based on the magnitude of the eigenvalues, determine one or more eigenvectors that contribute the most to the propagation of overall uncertainty in the system as the dominant propagation mode;

[0107] S43: Based on the spatial distribution characteristics of the dominant propagation mode, calculate the mean sensitivity and variance sensitivity of each node respectively; identify the node with high mean sensitivity as the propagation source, the node with high variance sensitivity as the key hub of the propagation channel, and the node with insufficient voltage margin as the weak end.

[0108] Furthermore, in step five, the step of determining at least one type of energy storage power station planning scheme based on the one or more dominant propagation modes is as follows: Pumped storage power stations are configured at propagation source nodes with high mean sensitivity, and the steady-state operating point is reconstructed through intraday energy time shift to adjust the power flow mean field and expand the safety margin of line power; electrochemical energy storage power stations are configured at key hub nodes of propagation channels with high variance sensitivity, and the spectral radius of the propagation matrix is ​​compressed through rapid power response to suppress power variance and reduce the fluctuation amplitude of line power.

[0109] Further, step S43 specifically involves: projecting the dominant propagation mode onto each node of the power grid topology, calculating the mean sensitivity and variance sensitivity respectively, and realizing the quantitative location of weak links and key hub nodes in the power grid;

[0110] Among them, mean sensitivity The following formula is used to evaluate the ability of a node to adjust to the expected value of line power flow:

[0111] (11);

[0112] Variance sensitivity The effect of node compression on the spectral norm of the propagation matrix is ​​defined according to the eigenvalue perturbation theory, as follows:

[0113] (12);

[0114] In the above formula, P i e is the injected power at node i; i Let i be the unit vector corresponding to node i; This represents the dominant mode; K is the feedback gain coefficient for energy storage.

[0115] A collaborative planning system for energy storage power stations based on uncertainty propagation analysis, as shown in the attached figure. Figure 2 As shown, it includes:

[0116] The data acquisition module is used to acquire the operating data of the power system, including the power grid topology, line impedance parameters, and historical data on the output and load of new energy sources.

[0117] The probabilistic power flow modeling module is used to construct an analytical AC probabilistic power flow model of the power system based on operational data; the analytical AC probabilistic power flow model is used to establish the analytical relationship between the statistical characteristics of system voltage and the statistical characteristics of line power.

[0118] The propagation characteristics analysis module is used to construct a propagation matrix that characterizes the propagation characteristics of system uncertainty based on the analytical AC probability power flow model, and to perform spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a dominant role in system uncertainty.

[0119] An energy storage planning module is used to determine a planning scheme for at least one type of energy storage power station based on one or more dominant propagation modes. The planning scheme includes the access location and capacity of the energy storage power station.

[0120] Example:

[0121] This embodiment uses a 220kV transmission system in a certain region as an example to explain in detail the planning method proposed in this invention. (See attached...) Figure 3 As shown, the system comprises 53 buses, 86 lines, and 30 generators (8 of which are external grid balancing nodes), with a total average load of approximately 1248MW. The system includes 4 pumped-storage / energy storage units, 3 wind turbines, and 7 photovoltaic units. Energy storage power stations are planned to be configured at 17 candidate nodes (nodes 10-26).

[0122] S101: Data Acquisition and Scene Division

[0123] First, historical operational data of the target power system is acquired, including time-series data such as node voltage, power injection, and line power flow recorded by the SCADA / EMS system, as well as the system's static topology and parameter data. In this embodiment, data with a 15-minute sampling period spanning two years is collected.

[0124] The massive amounts of collected data are preprocessed, including the removal of outliers and missing values. Then, clustering algorithms such as K-means are used to divide the annual operating data into several typical operating scenarios. The feature vectors for scenario division may include total wind power output, total photovoltaic power output, and total load level. In this embodiment, hierarchical K-means clustering is used, grouped by season (8 each for spring, summer, autumn, and winter), resulting in 32 typical scenarios. In addition, 144 extreme scenarios are identified (72 in category A with high load and low output, and 72 in category B with low load and high output), for a total of 176 analysis scenarios. Each scenario represents a typical system operating condition, and the frequency of occurrence of each scenario is calculated.

[0125] S102: Constructing an analytical communication probability power flow model

[0126] For each typical scenario, estimate the real and imaginary part vector of the bus voltage based on historical data samples for that scenario. The statistical properties of the mean vector Covariance Matrix Furthermore, statistical methods such as the KS test were used to verify whether it approximately follows a multivariate Gaussian distribution. .

[0127] Next, an analytical relationship between line power and voltage state is established. (Line) active power It can be precisely represented as a vector of voltages. The quadratic form:

[0128]

[0129] in, It is a quadratic coefficient matrix, whose elements are uniquely determined by the nodal admittance matrix and the line topology.

[0130] Under the assumption that the voltage vector follows a Gaussian distribution, the line power Expected E[P] l ] and variance Var(P l It has a closed-form analytic expression:

[0131]

[0132]

[0133] in, Represents the trace of a matrix.

[0134] To calculate the complete probability distribution of line power, its characteristic function is further derived. The closed-form solution is obtained. Then, by numerically integrating the characteristic function using the GilPelaez inversion formula, the cumulative distribution function of the line power can be efficiently obtained. Then, the probability of the line exceeding the limit is calculated. .

[0135] This step constructs a model from the source of uncertainty (represented by the voltage covariance matrix). From systemic risk (manifested as the probability of line exceeding limits) to systemic risk (manifested as the probability of line This method provides a complete and resolvable mathematical link, avoiding the huge computational overhead of traditional Monte Carlo simulations. In the 220kV system of this embodiment, the method calculates the probabilistic power flow of 86 lines in only about 0.08 seconds, which is about 1972 times faster than the approximately 167 seconds (2.8 minutes) of 10,000 Monte Carlo simulations; and about 197 times faster than the approximately 16.7 seconds of 1,000 Monte Carlo simulations, with an estimation error of less than 5% for the tail probability.

[0136] S103: Conduct uncertainty propagation characteristic analysis

[0137] To analyze the propagation of uncertainty at the system level, a system-level uncertainty index R is defined, which is the weighted sum of the power variances of all lines:

[0138]

[0139] Among them, weight It can be set according to the importance of the line or how close it is to the operating limit.

[0140] The system-level index R and the voltage covariance matrix Σ can be derived. V The relationship between these factors is established, and a key propagation matrix is ​​defined accordingly. To simplify the calculation, a low-rank decomposition of the voltage covariance matrix is ​​first performed. Then, define the propagation matrix M in the low-rank space. agg .

[0141] For the propagation matrix M agg Perform eigenvalue decomposition: .

[0142] This decomposition has a clear physical meaning:

[0143] eigenvalue λ k This measures the "amplification intensity" of the j-th propagation mode. The larger the eigenvalue, the greater the amplification of the voltage covariance as it propagates along that mode.

[0144] eigenvector ψ k The corresponding voltage fluctuation mode defines the kth propagation mode, which describes the spatial distribution and propagation path of uncertainty among grid nodes.

[0145] As attached Figure 4 In this embodiment, eigenvalue decomposition was performed on the propagation matrix of scene S3 (midday high light intensity). It was found that the first three eigenvalues ​​were much larger than the others, with modal participation factors of 41.7%, 37.2%, and 15.2%, respectively, and a cumulative contribution rate (MPF) of 94.1%. This indicates that the uncertainty propagation of the system is mainly controlled by the first two dominant modes (cumulative MPF = 78.9%), and the propagation mode is highly concentrated.

[0146] S104: Identify weak links and key nodes

[0147] The dominant mode that contributes the most For example (eigenvalue λ1 = 2.42 × 10⁻⁶), -7 The modal participation factor (MPF) was 41.7%, and its spatial distribution at each node of the power grid was analyzed.

[0148] Within the pre-defined candidate nodes (nodes 10-26), the top five nodes ranked by variance sensitivity are: node 10 (VSI=1.0000), node 26 (0.2264), node 11 (0.2054), node 16 (0.1777), and node 17 (0.1278). Among them, node 10 has a projected variance reduction potential of 0.08 and an electrical centrality of 8 (connecting 8 lines), making it a key hub for suppressing uncertainty propagation.

[0149] A combined analysis of mean sensitivity (MSI) and variance sensitivity (VSI) is shown in [reference needed]. Figure 5 Power grid nodes can be divided into three categories:

[0150] Sources of fluctuations: Nodes with high MSI, such as Node 12 (MSI=1.0000) and Node 23 (MSI=0.7488), are the main sources of fluctuations in new energy output.

[0151] Propagation bottlenecks: Nodes with high VSI, such as Node 10 (VSI=1.0000) and Node 26 (VSI=0.2264), are located at critical positions in the propagation path and are the main links in variance amplification.

[0152] Weak ends: Nodes 38, 39, and other terminal nodes are weak areas where uncertainties accumulate.

[0153] This result differs significantly from traditional sensitivity analysis conclusions: traditional methods identify critical nodes directly connected to renewable energy power plants (e.g., node 12), while the nodes with the highest propagation sensitivity are located at the "bottleneck" of the propagation path (e.g., node 10). This difference reveals that energy storage site selection should prioritize critical nodes in the propagation channel, rather than simply placing them at the source of fluctuations. Based on this, differentiated energy storage site selection recommendations are derived:

[0154] 1) Pumped storage power stations are suitable for regulating the expected value of power flow through intraday energy time shift, and nodes with high average sensitivity are preferred: nodes 12, 23, and 18;

[0155] 2) Electrochemical energy storage power stations are suitable for suppressing power fluctuations through fast response, and nodes with high variance sensitivity are preferred: nodes 10, 26, 11, 16, and 19;

[0156] S105: Collaborative Planning and Optimization of Energy Storage Power Stations

[0157] Based on the above propagation mechanism analysis, collaborative planning of energy storage is carried out. This invention reveals the differentiated action mechanisms of different types of energy storage:

[0158] Pumped storage power stations (PSHs) primarily function to alter the expected power flow distribution of the system by shifting energy over time, thus regulating the mean field. By placing a PSH at the propagation source and optimizing its intraday charging and discharging strategy, the expected power flow of critical lines can be proactively reduced from a high level (close to the limit), thereby providing a greater "safety margin" for uncertain fluctuations.

[0159] Electrochemical energy storage power stations, with their rapid response capabilities and closed-loop control, primarily function to absorb and release power in real time to smooth voltage fluctuations, i.e., suppress variance. Configuring a Base-Enhanced Energy Storage System (BESS) at critical nodes with high propagation sensitivity is equivalent to adding a "damper" to the propagation path, effectively attenuating the amplification of fluctuations during propagation.

[0160] Based on this collaborative mechanism, a two-stage energy storage optimization configuration model is established.

[0161] In the first stage, a small number of candidate nodes were selected based on the propagation sensitivity ranking, which greatly reduced the search space.

[0162] In the second stage, with the goal of minimizing the overall system over-limit risk and investment cost, capacity optimization is performed on the candidate solutions.

[0163] The final optimization result is: 400MW pumped storage will be deployed at nodes 50 and 10 respectively, and 400MW / 1600MWh electrochemical storage will be deployed at node 15.

[0164] After implementing this configuration, the BESS configuration reduced the spectral norm of the propagation matrix by 2.9%, and the synergistic effect of PSH+BESS was also 2.9%. (See...) Figure 6 Comparative experiments show that the proposed method reduces risk by 62.3%, an improvement of 21.7% compared to traditional optimization methods (51.0%), and significantly outperforms empirical methods (47.2%) and traditional sensitivity methods (54.7%). The proposed scheme demonstrates good robustness in all typical scenarios.

[0165] Although the present invention has been disclosed above with reference to preferred embodiments, these are not intended to limit the invention. Any person skilled in the art can make various changes or modifications without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention should be defined by the scope of the claims of this application.

Claims

1. A method for coordinated planning of energy storage power stations based on uncertainty propagation analysis, characterized in that: The method comprises the following steps: Step 1: obtaining operation data of the power system, wherein the operation data comprises power grid topology, line impedance parameters, new energy output and historical data of load of the power system; Step 2: constructing an analytical alternating current probability power flow model of the power system based on the operation data, wherein the analytical alternating current probability power flow model is used to establish an analytical relationship between statistical characteristics of system voltage and statistical characteristics of line power; Step 3: constructing a propagation matrix representing propagation characteristics of system uncertainty based on the analytical alternating current probability power flow model; Step 4: performing spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a leading role in system uncertainty; Step 5: determining a planning scheme of at least one type of energy storage power station based on the one or more dominant propagation modes, wherein the type of the planning scheme comprises an access position and a capacity of the energy storage power station.

2. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 1, characterized in that: Step 1 specifically comprises: obtaining historical data of a preset sampling period in a preset time period, performing abnormal data preprocessing on the historical data, and then classifying the preprocessed data into typical operation scenarios by using a clustering algorithm; a plurality of operation scenarios are obtained, each operation scenario represents a typical system operation condition, and the occurrence frequency of each operation scenario is calculated.

3. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 2, characterized in that: In step 2, the analytical alternating current probability power flow model of the power system specifically comprises: S21: for each operation scenario, estimating a bus voltage real and imaginary part vector V based on historical data samples in the scenario, which is expressed as follows: [ , ] T （1）； In the above formulae, , are the real and imaginary vectors of the node voltages, respectively; the superscript T denotes the transpose of a matrix. S22: Obtain the statistical characteristics of the full-network voltage vector V of the running scenario, and then obtain the mean vector and the covariance matrix ; verify whether it approximately obeys the multivariate Gaussian distribution ; S23: establish the analytical relationship of line power and voltage state corresponding to the operation scenario; the active power P of line l l is expressed as a quadratic form with respect to the voltage vector ​ （2）； where M l is the quadratic power coefficient matrix corresponding to the line l, whose elements are uniquely determined by the nodal admittance matrix and the line topology; S24: Assuming that the bus voltage real and imaginary part vectors obey a multivariate Gaussian distribution, with mean μ V and covariance matrix∑ V can be calculated from the grid normal operation using maximum likelihood estimation, and the expectation E[P l ], variance Var(P l ) and characteristic function of line l are derived as follows: （3）； （4）； （5）； In the above formula, tr(.) represents the trace of the matrix; i in the characteristic function represents an imaginary number; j is a number from 1 to n, and n is the total number of nodes included in the line; S25: Numerically integrate the characteristic function by the Gil Pelaez inversion formula to obtain the cumulative distribution function of the line power and then calculate the line out-of-limit probability a l， as follows: （6）； In the above formula, denotes the rated capacity of the line l.

4. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 3, characterized in that: In step 3, it specifically comprises: S31: as follows, define the uncertainty index R of the working scenario as the weighted sum of all line power variances contained in the corresponding working scenario; （7）； In the above formula, L is the total number of lines included in the working scenario; w l represents the importance weight of line I; as can be seen from the above formula, the uncertainty index R is a system-level uncertainty index; S32: Neglecting the second-order trace term, the voltage covariance matrix is decomposed as follows, and then the propagation matrix M is defined in the low-rank space agg , specifically: ) （8）； （9）； In the above equation,∑ inj represents the injection power covariance, whose value is calculated from the covariance matrix∑ V ; J is the Jacobian matrix.

5. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 4, characterized in that: Step 4 comprises: S41: Eigenvalue decomposition is performed on the propagation matrix M agg as follows: （10）； In the above formula, λ k , ψ k respectively represent the eigenvalue and eigenvector of M agg , respectively describe the propagation gain and propagation mode of system uncertainty; λ k measures the "amplification strength" of the kth propagation mode, the larger the eigenvalue, the higher the degree of amplification when the voltage covariance propagates along the mode; the eigenvector ψ K is the kth propagation mode, which describes the spatial distribution and propagation path of uncertainty among the nodes of the power grid; S42: according to the size of the eigenvalue, determine one or more eigenvectors with the largest contribution to the overall uncertainty propagation of the system as the dominant propagation mode; S43: according to the spatial distribution characteristics of the dominant propagation mode, respectively calculate the mean sensitivity and variance sensitivity of each node; identify the node with high mean sensitivity as the propagation source, identify the node with high variance sensitivity as the key hub of the propagation channel, and identify the node with insufficient voltage margin as the weak end.

6. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 1, characterized in that: In step 5, the determination of the planning scheme of at least one type of energy storage power station based on the one or more dominant propagation modes is: configuring pumped storage power stations at the propagation source nodes with high mean sensitivity to reconstruct the steady-state operating point through the time shift of the daily energy, adjust the mean field of the power flow, and expand the safety margin of the line power; configure the electrochemical energy storage power station at the key hub node of the propagation channel with high variance sensitivity, compress the spectral radius of the propagation matrix through the fast power response, suppress the power variance, and reduce the fluctuation amplitude of the line power.

7. The energy storage power station collaborative planning method based on uncertainty propagation analysis according to claim 5, characterized in that: Step S43 specifically comprises: projecting the dominant propagation mode to each node of the power grid topology, respectively calculating the mean sensitivity and variance sensitivity, and quantitatively locating the weak links and key hub nodes in the power grid; where the mean sensitivity The adjustment capability of the node to the line flow expectation value is evaluated as follows: （11）； Variance sensitivity For evaluating the compression effect of the node pair propagation matrix spectral norm, according to the eigenvalue perturbation theory, it is defined as follows: （12）； In the above formula, P i is the injection power of node i; e i is the unit vector corresponding to node i; represents the dominant mode; K is the feedback gain coefficient of energy storage.

8. A system for coordinated planning of energy storage power stations based on uncertainty propagation analysis, implemented by using the planning method according to any one of claims 1 to 7, characterized in that: The method comprises the following steps: A data acquisition module is configured to acquire operation data of the power system, the operation data including grid topology, line impedance parameters, and historical data of new energy output and load; A probabilistic power flow modeling module is configured to construct an analytical AC probabilistic power flow model of the power system based on the operation data, the analytical AC probabilistic power flow model being configured to establish an analytical relationship between system voltage statistical characteristics and line power statistical characteristics; A propagation characteristic analysis module is configured to construct a propagation matrix representing propagation characteristics of system uncertainties based on the analytical AC probabilistic power flow model, and perform spectral analysis on the propagation matrix to identify one or more dominant propagation modes that play a leading role in system uncertainties; An energy storage planning module is configured to determine a planning scheme of at least one type of energy storage power station based on the one or more dominant propagation modes, the planning scheme including an access location and capacity of the energy storage power station.

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