Robust security region analysis method for electrical integrated energy systems considering renewable energy uncertainty

Abstract

The application provides a robust security domain analysis method of an electrical integrated energy system considering renewable energy uncertainty, and belongs to the technical field of electrical integrated energy systems; solves the problem that existing security domain analysis methods are difficult to balance calculation efficiency and robustness; the method comprises the following steps: a large number of random output scenes of renewable energy are extracted by using a Latin hypercube sampling method, similar scenes are clustered by Euclidean distance through K-means clustering, a typical scene set is generated to reduce the amount of calculation; the dynamic security domain of the electrical integrated energy system under each typical scene is calculated by a radial orbit sampling method, and the safe operation boundary in different directions is described; the intersection of the dynamic security domains of all typical scenes is taken as the robust security domain, and it is ensured that the system safety constraint is met under any renewable energy fluctuation scene; the application is applied to the security domain analysis of the electrical integrated system containing renewable energy.

Description

Technical Field

[0001] This application relates to the field of integrated electrical energy systems, and in particular to a robust security domain analysis method for integrated electrical energy systems that takes into account the uncertainty of renewable energy. Background Technology

[0002] In recent years, the penetration rate of renewable energy has shown a significant upward trend. The output of renewable energy is largely dependent on weather conditions, thus exhibiting characteristics of randomness, volatility, and intermittent output. This often leads to substantial prediction errors in the operating status of Integrated Electricity-Gas Systems (IEGS). While the security region method can obtain the complete region where the system can operate safely, and its application in power systems is relatively mature, the uncertainty of renewable energy output means that both traditional Steady-State Security Region (S-SR) methods based on steady-state energy flow models and traditional Dynamic Energy Flow Model-based Security Region (D-SR) methods have corresponding shortcomings when applied to the security region of IEGS.

[0003] Specifically, the IEGS security domain is the intersection of the Electric Power System (EPS) security domain and the Natural Gas System (NGS) security domain. However, the power flow in EPS and the natural gas flow in NGS differ significantly in physical properties. Electricity flows propagate at near the speed of light, allowing power injection from generators within EPS to be instantaneously transmitted to the load, thus promptly mitigating changes in load demand. Therefore, the EPS security domain is primarily determined by the current operating state of the system. Unlike electricity flows, natural gas flows propagate quite slowly; natural gas produced from wells within NGS typically takes several hours to reach the load. In actual operation, NGS supports the load's natural gas demand through gas storage in adjacent pipelines. Therefore, the NGS security domain is closely related to the distribution of natural gas flows within the pipeline network. However, due to the time-lag characteristics of natural gas, the distribution of natural gas flows in NGS depends not only on the current operating state of the system but also on its historical flow distribution. This gives the NGS security domain a cumulative characteristic, meaning it is jointly determined by the current and historical operating states of the system.

[0004] Influenced by the NGS safety domain, the IEGS safety domain also exhibits a cumulative characteristic over time. Its range depends not only on the system's boundary conditions within the current runtime but also on the energy flow distribution state within the system. Therefore, in actual operation, the IEGS safety domain dynamically evolves as the runtime progresses and the energy flow distribution state changes, making the traditional S-SR method unable to accurately assess the safety margin of the IEGS. Figure 1 As shown, , and These represent the numbers in IEGS respectively. and The gas-fired generator unit (PG) in the gas-fired generator unit (GFU) is in dispatch time There are three different safe operating points. Assuming the system's gas load gradually increases its demand for natural gas, the pipeline storage reserves in the NGS will be consumed accordingly, causing a drop in node gas pressure. This will gradually limit the natural gas supply from the NGS to the GFU, thus gradually shrinking the safety domain of the IEGS. In subsequent scheduling moments, and Each point gradually becomes an unsafe operating point. Steady-state energy flow models have significant biases in calculating natural gas flow and cannot calculate pipeline storage capacity within the NGS. Therefore, the traditional S-SR method cannot characterize the aforementioned dynamic evolution process of the IEGS safety domain, leading to misjudgments of IEGS safety margins and operating point safety, thus posing safety risks during actual IEGS scheduling. Therefore, it is necessary to quantitatively assess the impact of dynamic energy flow operating characteristics on the IEGS safety domain in order to provide accurate and reliable safety margin information for IEGS scheduling instructions throughout the entire operating cycle.

[0005] The Distributed Energy Regulator (D-SR) is defined as the maximum energy injection space of the IEGs (Integrated Energy Grids) in each operating segment throughout the entire operating cycle, under the premise of satisfying dynamic energy flow balance constraints and system operation safety constraints. The D-SR is updated on a rolling basis at each scheduling moment based on the real-time changes in the IEGs energy flow distribution state within each operating segment to ensure the accuracy of real-time assessment of changes in the IEGs safety margin. However, traditional D-SRs are constructed based on fixed IEGs operating state prediction data. Due to the inherent randomness, volatility, and intermittent output characteristics of renewable energy, the operating state of IEGs often has significant prediction errors. This means that the safe operating point generated by the D-SR may violate system safety constraints in actual operation.

[0006] Within the framework of stochastic programming, IEGS requires transforming continuous uncertainties (such as the probability distributions of wind speed and irradiance) into a finite set of discrete scenarios through scenario generation. Existing methods typically employ Monte Carlo sampling (MCS) to generate these scenario sets; however, MCS requires generating extremely large-scale scenarios to ensure the accuracy of the probability distributions, resulting in low computational efficiency. Furthermore, the multi-energy flow coupling and time-delay characteristics of IEGS further increase the complexity of solving high-dimensional security domains, making it difficult for existing methods to balance computational efficiency and robustness. Therefore, developing an efficient and accurate robust security domain analysis method for integrated electrical energy systems is of great significance for ensuring the safe and economical operation of the system. Summary of the Invention

[0007] To address the aforementioned technical issues, this application proposes a robust security domain analysis method for an integrated electrical energy system that takes into account the uncertainties of renewable energy sources.

[0008] The technical solution adopted in this application is: a robust security domain analysis method for an integrated electrical energy system that takes into account the uncertainty of renewable energy, comprising the following steps:

[0009] S1: The Latin hypercube sampling method is used to extract random power output scenarios of renewable energy. Then, similar scenarios are clustered according to Euclidean distance through K-means clustering to generate a typical scenario set.

[0010] S2: The dynamic safety domain of the integrated electrical energy system under various typical scenarios is calculated using the radial orbit sampling method or the weighted coefficient allocation method, characterizing the safe operation boundary in different directions. In the low-dimensional energy injection space, the robust boundary points of the system in different energy injection directions are solved using the radial orbit sampling method, and the robust safety domain for different scheduling periods is solved based on this, thereby constructing the robust safety domain of the integrated electrical energy system throughout the entire operating cycle. In the high-dimensional energy injection space, the safety domain in the high-dimensional space is reduced to a one-dimensional optimization problem by using the weighted coefficient allocation method, quickly calculating the upper and lower limits of the safe power of each node under a fixed scheduling ratio, and thereby realizing a visual assessment of the global safety margin.

[0011] S3: Take the intersection of the dynamic safety domains of all typical scenarios as the robust safety domain.

[0012] Furthermore, the specific implementation process of using the Latin hypercube sampling method to extract a large number of random power output scenarios from renewable energy sources in step S1 includes:

[0013] S101: Generating the initial sampling matrix for renewable energy using the Latin hypercube sampling method. Initial sampling matrix The correlation between rows is expressed by a correlation coefficient matrix. Characterization, further, uses the correlation coefficient matrix The root mean square characterizes the initial sampling matrix. The degree of correlation between the rows within the same section;

[0014] S102: Reducing the initial sampling matrix based on Cholesky decomposition method Correlation between random variables in each row: Construct a permutation matrix Each row vector within it consists of randomly arranged integers from 1 to N, and the values ​​of the elements in each row represent the initial sampling matrix. Calculate the permutation matrix based on the arrangement positions of the elements in the corresponding rows. Correlation coefficient matrix between rows The correlation coefficient matrix was then decomposed using the Cholesky method. Decomposed into a non-singular lower triangular matrix Based on triangular matrix Arrange the matrix Reconstructed into a matrix where each row is independent ;

[0015] S103: Rearrange the elements in each row of the current sampling matrix according to the ascending order of the corresponding elements in matrix G; construct a new sampling matrix based on the rearranged result; calculate the correlation between each row of the new sampling matrix until the root mean square of the correlation coefficient of the obtained sampling matrix is ​​less than the target value. At this point, the random original scene set of renewable energy is obtained. .

[0016] Furthermore, the specific implementation process of generating a typical scene set by clustering similar scenes according to Euclidean distance using K-means clustering in step S1 includes:

[0017] S111: Select the original scene set Maximum inner distance Each scenario serves as the initial cluster center. And all original scenes are assigned to the cluster corresponding to the nearest center, thereby constructing A typical cluster of original scenarios;

[0018] S112: Based on the cluster assignment results, recalculate the cluster centers for each cluster:

[0019] ;

[0020] In the formula, For the first During the nth iteration Representative scenarios for each cluster; For the first During the nth iteration The original scene set within each cluster; For the first During the nth iteration The number of scenarios contained in each cluster;

[0021] Calculate the deviation of cluster centers between two iterations :

[0022] ;

[0023] S113: Reassign clusters based on the cluster centers of the current iteration, repeat S112, and define the convergence tolerance. until If the cluster assignment of the original scene no longer changes, the iteration stops, and the cluster center scenes of each cluster are output, thus forming a typical random scene set for renewable energy. .

[0024] Furthermore, the specific implementation process of step S2 includes:

[0025] S201: Random Scene The dynamic security domain of China Electric's integrated energy system is:

[0026] ;

[0027] In the formula, Represents a random scenario The D-SR of IEGS, where IEGS stands for Integrated Electrical and Energy Systems and D-SR stands for Dynamic Security Domain; and Random scenes IEGS during scheduling period The set of control variables and the set of state variables within; For random scenarios Next scheduling period Renewable energy output vector within; The requirements that D-SR must meet regarding Set of equality constraints; The requirements that D-SR must meet regarding Set of inequality constraints;

[0028] S202: Based on the dynamic security domain under a single random scenario, the robust security domain of the integrated electrical energy system is:

[0029] ;

[0030] In the formula, R-SR represents IEGS, and R-SR stands for Robust Security Domain; For random scenarios Download IEGS's D-SR.

[0031] Furthermore, the safety boundary of R-SR in the low-dimensional energy injection space is solved based on the radial orbit sampling method. That is, under the premise of satisfying the system operation constraints under each stochastic scenario, the IEGS is solved for each feasible low-dimensional energy injection adjustment direction. Robust safety margin on:

[0032] ;

[0033] ;

[0034] In the formula, The requirements that D-SR must meet regarding The set of equality constraints; The requirements that D-SR must meet regarding The set of inequality constraints; For IEGS during the scheduling period The set of baseline control variables within, For IEGS during the scheduling period The set of baseline state variables within; For random scenarios Next scheduling period Internal IEGS in direction Safety margin; For scheduling period Internal IEGS in direction Robust safety margin, i.e. Each running point within can be used by any random scenario. Down Included;

[0035] Therefore, the above two equations can be rewritten as:

[0036] ;

[0037] ;

[0038] In the formula: and Distributed to scheduling periods Internal IEGS in direction Robust upper boundary point and robust lower boundary point; and Random scenes Next scheduling period Internal IEGS in direction The upper and lower boundary points.

[0039] Furthermore, by using the weight coefficient allocation method, the safety domain in the high-dimensional space is reduced to a one-dimensional optimization problem, which is solved through the following optimization solution model:

[0040] ;

[0041] ;

[0042] In the formula, For scheduling period Internal IEGS in random scenarios Global security margin; For scheduling period Global robust safety margin of internal IEGS; By adjusting the direction of energy injection into higher dimensions, the above two equations can be rewritten as:

[0043] ;

[0044] ;

[0045] In the formula, and Distributed to scheduling periods Robust upper and lower boundary points of the inner IEGS; and Distributed to scheduling periods Internal IEGS in random scenarios The upper and lower boundary points in the equation.

[0046] Furthermore, the robust boundary points for each scheduling period are solved using the radial orbit sampling method. The parameters involved include the structural topology and equipment parameters of the integrated electrical energy system, the maximum orbit rotation coefficient, the operating cycle, and the initial energy flow distribution state of the integrated electrical energy system.

[0047] Furthermore, renewable energy includes wind power and solar power.

[0048] The advantages of this application compared to existing technologies are as follows: This application utilizes Latin hypercube hierarchical sampling in statistics to extract scenarios of random power output from renewable energy sources. To reduce computational load, K-means clustering is used to group scenarios with similar Euclidean distances into a single cluster. Radial orbit sampling is used to calculate the upper and lower bounds of operational safety in each direction under typical scenarios to form a safety domain. The intersection of all typical scenarios is taken as the robust safety domain of the electrical interconnection system, ensuring that system safety constraints are met under any renewable energy fluctuation scenario. Numerical examples demonstrate that this method significantly improves computational efficiency, and R-SR can effectively characterize the safety margin in uncertain operating conditions, avoiding the conservative shortcomings of traditional D-SR. Attached Figure Description

[0049] The following description, in conjunction with the accompanying drawings, further illustrates this application:

[0050] Figure 1 A schematic diagram illustrating the dynamic evolution of security domains in IEGS;

[0051] Figure 2 A flowchart illustrating the method provided in this application embodiment;

[0052] Figure 3 This is a schematic diagram of equally spaced LHS sampling provided in an embodiment of this application;

[0053] Figure 4 This application provides a network topology diagram for IEGS nodes 39-20.

[0054] Figure 5 A comparison diagram of R-SR and D-SR provided for embodiments of this application. Detailed Implementation

[0055] like Figures 2 to 5 As shown, this application provides a robust security domain analysis method for an integrated electrical energy system that takes into account the uncertainty of renewable energy sources, including the following steps:

[0056] S1: The Latin hypercube sampling (LHS) method is used to extract a large number of random power output scenarios of renewable energy. Then, K-means clustering is used to group similar scenarios according to Euclidean distance to generate a typical scenario set to reduce the amount of computation.

[0057] S2: The dynamic safety domain (D-SR) of the integrated electrical energy system under various typical scenarios is calculated using the radial orbit sampling method or the weighted coefficient allocation method to characterize the safe operating boundary in different directions. In the low-dimensional energy injection space, the robust boundary points of the system in different energy injection directions are solved using the radial orbit sampling method. Based on this, the robust safety domain for different scheduling periods is solved, thereby constructing the robust safety domain of the integrated electrical energy system throughout its entire operating cycle. In the high-dimensional energy injection space, the safety domain in the high-dimensional space is reduced to a one-dimensional optimization problem using the weighted coefficient allocation method, which quickly calculates the upper and lower limits of the safe power of each node under a fixed scheduling ratio, and thus realizes a visual assessment of the global safety margin.

[0058] S3: Take the intersection of the dynamic security domains of all typical scenarios as the Robust Security Region (R-SR), which represents the dynamic security domain of the integrated electrical energy system under the uncertainty of renewable energy scenarios, and ensures that the system security constraints are met under any renewable energy fluctuation scenario.

[0059] This embodiment takes the uncertainty of wind turbine output as an example, and uses the Latin hypercube sampling method and K-means clustering method to construct stochastic operating scenarios of IEGS that include the uncertainty characteristics of renewable energy. A robust R-SR model for predicting IEGS operating status errors is then constructed by using the intersection of D-SRs under each typical scenario to characterize the impact of renewable energy uncertainty on day-ahead scheduling of IEGS. It should be noted that constructing the IEGS R-SR based on typical stochastic scenarios significantly reduces the computational burden, making it applicable to day-ahead pre-scheduling problems of large-scale complex IEGS. Furthermore, it avoids interference from low-probability, high-intensity scenarios on the R-SR solution, thereby reducing the conservatism of pre-scheduling decisions. In addition, the method of constructing the stochastic scenario set considering only wind power uncertainty does not affect the generality of the proposed R-SR. Uncertainties in photovoltaic output and load demand can be based on their stochastic distribution characteristics, using the same sampling method to construct corresponding stochastic scenario sets, which can be conveniently incorporated into the constraint set of the R-SR.

[0060] The output of wind turbines is affected by parameters such as wind speed, wind direction, air pressure, and temperature in their environment. Among these, the random distribution of wind speed is a key factor leading to the uncertainty in wind turbine output. Currently, both academia and industry widely use the classic two-parameter Weibull distribution to fit the probability distribution model of wind speed. Extensive experimental data shows that the Weibull distribution is suitable for fitting and representing wind speed models under most meteorological and topographical conditions. Its probability density function and cumulative distribution function can be described as follows:

[0061] (1);

[0062] (2);

[0063] In the formula, and Let these represent the probability density function and cumulative distribution function of the wind speed probability distribution, respectively. For predicted wind speed, the unit is m / s; and Let be the scale parameter and shape parameter of the wind speed probability distribution, respectively, satisfying... , These two values ​​represent the amplitude and shape of random fluctuations in wind speed, respectively. Their values ​​are related to the environment of the area where the wind turbine is located and can be obtained by numerical methods such as the maximum likelihood method based on historical data.

[0064] Based on the probability distribution model of wind speed, the stochastic distribution model of wind turbine output can be constructed as follows:

[0065] (3);

[0066] In the formula, The power output function of a wind turbine as a function of wind speed; , and These are the cut-in wind speed, cut-out wind speed, and rated wind speed of the wind turbine, respectively, in m / s; This refers to the rated power of the wind turbine, expressed in watts (W).

[0067] Based on this, a random sampling method is used to construct a set of possible wind power output scenarios. Existing research typically uses MCS or LHS to generate a randomized original scenario set for probability distribution models. MCS is essentially a simple random sampling method based on the law of large numbers. When the sample size is small, this sampling method may struggle to characterize the true probability distribution of random variables. Therefore, MCS requires constructing an extremely large randomized original scenario set, which reduces the computational efficiency of the model. LHS, on the other hand, is a stratified sampling method. This method first stratifies the sample space and then performs random sampling within each sample space. This ensures the independence of the sampling results and uniform coverage of the sample space. Therefore, LHS can accurately characterize the true probability distribution of random variables with a smaller sample size. Therefore, this embodiment uses LHS to construct a randomized original scenario set for wind power output.

[0068] The process of constructing the set of uncertain output scenarios for wind turbines is as follows:

[0069] Assuming the wind turbine unit contains a total of The output random variable, of which the first... random variables cumulative distribution function Its inverse function exists. yes arrive The mapping relationship can be expressed as:

[0070] (4);

[0071] random variable The cumulative distribution function curve is as follows Figure 3 As shown. Figure 3 middle, This represents the size of the sampling, or the total number of scenes generated by random sampling. The vertical axis of the cumulative distribution function curve has the following values: Divided into A sampling interval with equal spacing and no overlap, i.e. , , ..., Find the midpoint of each numerical interval. The corresponding inverse function As a sample of this interval, its sampled value can be expressed as:

[0072] (5);

[0073] Random variables obtained from sampling Corresponding to a containing Row vector of elements Therefore, a initial sampling matrix :

[0074] (6);

[0075] Initial sampling matrix The correlation between rows can be achieved through a Correlation coefficient matrix Characterization:

[0076] (7);

[0077] (8);

[0078] In the formula, For the initial sampling matrix The Line and number Correlation coefficient between rows; This represents the covariance operator.

[0079] Furthermore, using the correlation coefficient matrix The root mean square characterizes the initial sampling matrix. The degree of correlation between lines within the same line:

[0080] (9).

[0081] Based on this, the initial sampling matrix is ​​reduced using the Cholesky decomposition method. The correlation between random variables in each row of the sample matrix. The principle of this method is to use the initial sampling matrix... The elements within the array are arranged in random order, while maintaining their individual values. To achieve this, a... Permutation matrix Each row vector within it consists of randomly arranged integers from 1 to N, and the values ​​of the elements in each row represent the initial sampling matrix. The permutation matrix is ​​calculated by determining the position of the elements in the corresponding row. Correlation coefficient matrix between rows And the matrix is ​​decomposed using Cholesky decomposition. Decomposed into a non-singular lower triangular matrix The two satisfy the following relationship:

[0082] (10);

[0083] Due to the triangular matrix It is non-singular, therefore its inverse matrix exists. Based on triangular matrices. Permutation matrix It can be refactored into a row-independent structure. matrix :

[0084] (11).

[0085] Due to the matrix The elements in the initial sampling matrix are not necessarily positive integers; therefore, the initial sampling matrix... The elements in each row are in matrix form The elements in each row are rearranged in ascending order to construct a new sampling matrix. The correlation between rows of the new sampling matrix can be calculated using equations (7)-(9). This process is repeated until the root mean square correlation coefficient of the obtained sampling matrix is ​​reached. Less than the target value. At this point, the wind turbine output is randomized across the original scene set. The construction is complete, and the data vector representation of any random wind turbine output scenario is as follows: That is, the original scene set It contains N possible wind turbine output scenarios.

[0086] To further reduce the computational burden, it is usually necessary to reduce the number of random original scenarios, that is, to use as few typical scenarios as possible to represent the uncertainty characteristics of wind turbine output to the greatest extent. Therefore, this embodiment uses a K-means clustering algorithm based on Euclidean distance to divide the original scenarios of wind turbine output into several different clusters, and reduces the set of original scenarios within each cluster to a typical scenario that can represent the characteristics of that cluster, thereby constructing a set of typical scenarios that can effectively represent the original random characteristics of wind turbine output. The Euclidean distance between each scenario is... It can be characterized as:

[0087] (12);

[0088] In the formula, and The first The and the first A random scenario; and The first The and the first The first random scenario A random variable.

[0089] Based on Euclidean distance First, select the original scene set. Maximum inner distance Each scenario serves as the initial cluster center. And all original scenes are assigned to the cluster corresponding to the nearest center, thereby constructing The typical clusters of the original scene are then identified. Based on the cluster assignment results, the cluster centers of each cluster are recalculated.

[0090] (13);

[0091] In the formula, For the first During the nth iteration Representative scenarios for each cluster; For the first During the nth iteration The original scene set within each cluster; For the first During the nth iteration The number of scenarios contained in each cluster.

[0092] In addition, the deviation of cluster centers between two iterations is calculated. :

[0093] (14).

[0094] Finally, the clusters are reassigned based on the cluster centers of the current iteration, the cluster centers of each cluster are recalculated according to equation (13), and the deviation of the cluster centers between the two iterations is calculated according to equation (14). Define convergence tolerance. until If the cluster assignment of the original scene no longer changes, the iteration stops, and the cluster center scenes of each cluster are output, thus forming a typical random scene set of wind turbine output. .

[0095] Based on the aforementioned typical random scenario set of wind turbine output The R-SR of IEGS can be described as the system contained in The intersection of D-SR in various typical scenarios. Specifically, random scenarios. The D-SR of IEGS can be constructed as follows:

[0096] (15);

[0097] In the formula, Represents a random scenario Download IEGS's D-SR; and Random scenes IEGS during scheduling period The set of control variables and the set of state variables within; For random scenarios Next scheduling period The internal fan output vector; The requirements that D-SR must meet regarding Set of equality constraints; The requirements that D-SR must meet regarding Set of inequality constraints.

[0098] Based on the D-SR in a single random scenario, the R-SR of IEGS can be constructed as follows:

[0099] (16);

[0100] In the formula, R-SR represents IEGS; For random scenarios Download IEGS's D-SR.

[0101] The safety boundary of R-SR in the low-dimensional energy injection space can be solved based on the radial orbit sampling method. That is, under the premise of satisfying the system operation constraints under each stochastic scenario, the IEGS is solved for each feasible low-dimensional energy injection adjustment direction. Robust safety margin on:

[0102] (17);

[0103] (18);

[0104] In the formula, The requirements that D-SR must meet regarding Set of equality constraints; The requirements that D-SR must meet regarding Set of inequality constraints; For IEGS during the scheduling period The set of baseline control variables within, The set of baseline state variables for IEGS during the scheduling period τ; For random scenarios Next scheduling period Internal IEGS in direction Safety margin; For scheduling period Internal IEGS in direction Robust safety margin, i.e. Each running point within can be used by any random scenario. Down Therefore, equations (17) and (18) can be rewritten as:

[0105] (19);

[0106] (20);

[0107] In the formula: and Distributed to scheduling periods Internal IEGS in direction Robust upper boundary point and robust lower boundary point; and Random scenes Next scheduling period Internal IEGS in direction The upper and lower boundary points.

[0108] Based on equations (17) and (18), an R-SR optimization algorithm for IEGS can be constructed. The specific algorithm steps are as follows:

[0109] 1. Parameter settings: Set the IEGS structure topology and equipment parameters, and the maximum number of track rotations. and operating cycle .

[0110] 2. Initialization, specifically including:

[0111] 1) Construct using LHS and K-means clustering methods A typical scenario of random power output from renewable energy sources;

[0112] 2) Set scheduling period index and rotation number index ;

[0113] 3) Set the initial energy flow distribution state of IEGS. .

[0114] 3. Optimization solution for the robust safety region boundary, including the following steps:

[0115] 1) Perform the following outer loop steps:

[0116] 2) Set the scheduling time for IEGS The set of baseline control variables ;

[0117] 3) Calculate the rotation angle and rotation angle step ;

[0118] 4) Execute the following inner loop steps:

[0119] 5) Based on scheduling period index Set the direction of low-dimensional energy injection adjustment. ;

[0120] 6) Solve for IEGS using equations (19) and (20) Robust boundary points on and ;

[0121] 7) Number of orbital rotations and update the rotation angle. ;

[0122] 8) Calculate and update the low-dimensional energy injection adjustment direction. ;

[0123] 9) Until: the number of orbital rotations reaches the upper limit. ;

[0124] 10) Constructing IEGS based on robust boundary point sets during scheduling periods R-SR within;

[0125] 11) Based on R-SR and the optimal scheduling objective, solve for IEGS during the scheduling period. running points within ;

[0126] 12) Based on IEGS during scheduling periods Energy flow distribution state update at the end time ;

[0127] 13) Advance scheduling period, i.e. ;

[0128] 14) Until: the scheduling period reaches its upper limit. .

[0129] In the solution part of step 3, steps 1) to 14) constitute the outer loop, and steps 4) to 9) constitute the inner loop. The outer loop traverses each scheduling period of the IEGS within the operating cycle, and the inner loop solves for the robust boundary points of the IEGS in each energy injection adjustment direction within each scheduling period, thereby constructing the R-SR of the IEGS throughout the entire operating cycle.

[0130] Furthermore, for the problem of reducing the order of R-SR in a high-dimensional energy-occupying space, the following optimized solution model is constructed:

[0131] (twenty one);

[0132] (twenty two);

[0133] In the formula, For scheduling period Internal IEGS in random scenarios Global security margin; For scheduling period Global robust safety margin of internal IEGS; The direction of energy injection into higher dimensions is adjusted. Therefore, equations (21) and (22) can be rewritten as:

[0134] (twenty three);

[0135] (twenty four);

[0136] In the formula, and Distributed to scheduling periods Robust upper and lower boundary points of the inner IEGS; and Distributed to scheduling periods Internal IEGS in random scenarios The upper and lower boundary points in the equation.

[0137] Due to the adjustment of the direction of high-dimensional energy injection in equation (22) Since the given value is used, equations (23) and (24) can be solved directly without using the radial orbit rotation method, thereby achieving a global evaluation of R-SR in IEGS.

[0138] To verify the effectiveness of the proposed R-SR model and optimization solution method for IEGS in this application, simulation analysis is conducted based on an IEGS case study. The case study involves a large-scale IEGS with 39 EPS nodes and 20 NGS nodes. R-SR analysis was performed on this large-scale IEGS, verifying the effectiveness of the proposed method for assessing the security domain of large-scale IEGS, and exploring the impact of renewable energy uncertainties on the security domain of IEGS. All case simulations were coded using the YALMIP toolbox in MATLAB software and solved using CPLEX 12.8.0 on a computer configured with an Intel i5-10400 CPU and 16GB of memory.

[0139] The IEGS network topology of nodes 39-20 in the case is as follows: Figure 4 As shown, the EPS includes two types of generator units: coal-fired power units (CFUs) and gas-fired power units (GFUs). Units C1, C2, G2, and G3 have a rated power of 400MW, while units C3, C4, G1, and G4 have a rated power of 200MW. The gas supply pressure from natural gas wells S1 and S2 in the NGS is 60 bar. This case study sets up one scheduling period. Due to the large scale of the NGS, to analyze the impact of natural gas flow time lag characteristics and pipeline storage capacity on the dynamic evolution of the IEGS security domain, the scheduling period length is set to 4 hours, i.e., the total operating cycle is 4 hours. The total electrical load during the scheduling period is 2494MW, the natural gas load demand is 653MW, and the wind power plant output is 825MW.

[0140] Taking gas-fired generator units G2, G3, and G4, and coal-fired generator units C3 and C4, located at the end nodes of the NGS pipeline network, as the objects of operational safety margin assessment, the D-SR of each unit is established based on the improved D-SR reduction solution method.

[0141] Furthermore, 500 random wind power output scenarios were generated based on the LHS method, and four typical random scenarios were extracted using the K-means clustering method, as shown in Table 1. Based on this, D-SRs of IEGS were constructed for each typical scenario.

[0142] Table 1 Total power output of wind turbines in various typical random scenarios

[0143] .

[0144] Based on the different D-SRs of IEGS in various typical scenarios, an R-SR of IEGS considering the uncertainty of wind power output is constructed. For example... Figure 5 As shown, the resulting R-SR is generally a subset of the D-SR in the original scenario, and the allowable output range of each unit in the R-SR is generally smaller than that in the D-SR. This means that the uncertainty of wind power output necessitates that IEGS reserve sufficient adjustable capacity of unit output to smooth out potential source-load supply and demand fluctuations, thus imposing stricter constraints on the safe operating range of the units. In summary, under conditions of large fluctuations in wind power output, the safe operating point in the original D-SR may no longer be safe. Therefore, for the uncertain pre-scheduling problem of IEGS in the day-ahead phase, it is necessary to use the R-SR method to characterize the robust safe operating range of each generator unit.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy, characterized in that: Includes the following steps: S1: The Latin hypercube sampling method is used to extract random power output scenarios of renewable energy. Then, similar scenarios are clustered according to Euclidean distance through K-means clustering to generate a typical scenario set. S2: The dynamic safety domain of the integrated electrical energy system under various typical scenarios is calculated using the radial orbit sampling method or the weighted coefficient allocation method, characterizing the safe operation boundary in different directions. In the low-dimensional energy injection space, the robust boundary points of the system in different energy injection directions are solved using the radial orbit sampling method, and the robust safety domain for different scheduling periods is solved based on this, thereby constructing the robust safety domain of the integrated electrical energy system throughout the entire operating cycle. In the high-dimensional energy injection space, the safety domain in the high-dimensional space is reduced to a one-dimensional optimization problem by using the weighted coefficient allocation method, quickly calculating the upper and lower limits of the safe power of each node under a fixed scheduling ratio, and thereby realizing a visual assessment of the global safety margin. S3: Take the intersection of the dynamic safety domains of all typical scenarios as the robust safety domain.

2. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy, as described in claim 1, is characterized in that: The specific implementation process of using the Latin hypercube sampling method to extract a large number of random power output scenarios of renewable energy in step S1 includes: S101: Generating the initial sampling matrix for renewable energy using the Latin hypercube sampling method. Initial sampling matrix The correlation between rows is expressed by a correlation coefficient matrix. Characterization, further, uses the correlation coefficient matrix The root mean square characterizes the initial sampling matrix. The degree of correlation between the rows within the same section; S102: Reducing the initial sampling matrix based on Cholesky decomposition method Correlation between random variables in each row: Construct a permutation matrix Each row vector within it consists of randomly arranged integers from 1 to N, and the values ​​of the elements in each row represent the initial sampling matrix. Calculate the permutation matrix based on the arrangement positions of the elements in the corresponding rows. Correlation coefficient matrix between rows The correlation coefficient matrix was then decomposed using the Cholesky method. Decomposed into a non-singular lower triangular matrix Based on triangular matrix Arrange the matrix Reconstructed into a matrix where each row is independent ; S103: Rearrange the elements in each row of the current sampling matrix according to the ascending order of the corresponding elements in matrix G; construct a new sampling matrix based on the rearranged result; calculate the correlation between each row of the new sampling matrix until the root mean square of the correlation coefficient of the obtained sampling matrix is ​​less than the target value. At this point, the random original scene set of renewable energy is obtained. .

3. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy, as described in claim 2, is characterized in that: The specific implementation process of generating a typical scene set by clustering similar scenes according to Euclidean distance using K-means clustering in step S1 includes: S111: Select the original scene set Maximum inner distance Each scenario serves as the initial cluster center. And all original scenes are assigned to the cluster corresponding to the nearest center, thereby constructing A typical cluster of original scenarios; S112: Based on the cluster assignment results, recalculate the cluster centers for each cluster: ； In the formula, For the first During the nth iteration Representative scenarios for each cluster; For the first During the nth iteration The collection of original scenes within each cluster; For the first During the nth iteration The number of scenarios contained in each cluster; Calculate the deviation of cluster centers between two iterations : ； S113: Reassign clusters based on the cluster centers of the current iteration, repeat S112, and define the convergence tolerance. until If the cluster assignment of the original scene no longer changes, the iteration stops, and the cluster center scenes of each cluster are output, thus forming a typical random scene set for renewable energy. .

4. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy sources according to claim 3, characterized in that: The specific implementation process of step S2 includes: S201: Random Scene The dynamic security domain of China Electric's integrated energy system is: ； In the formula, Represents a random scenario The D-SR of IEGS, where IEGS stands for Integrated Electrical and Energy Systems and D-SR stands for Dynamic Security Domain; and Random scenes IEGS during scheduling period The set of control variables and the set of state variables within; For random scenarios Next scheduling period Renewable energy output vector within; The requirements that D-SR must meet regarding Set of equality constraints; The requirements that D-SR must meet regarding Set of inequality constraints; S202: Based on the dynamic security domain under a single random scenario, the robust security domain of the integrated electrical energy system is: ； In the formula, R-SR represents IEGS, and R-SR stands for Robust Security Domain; For random scenarios Download IEGS's D-SR.

5. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy sources according to claim 4, characterized in that: The safety boundary of R-SR in the low-dimensional energy injection space is solved based on the radial orbit sampling method. That is, under the premise of satisfying the system operation constraints under various stochastic scenarios, the IEGS is solved for each feasible low-dimensional energy injection adjustment direction. Robust safety margin on: ； ； In the formula, The requirements that D-SR must meet regarding The set of equality constraints; The requirements that D-SR must meet regarding The set of inequality constraints; For IEGS during the scheduling period The set of baseline control variables within, For IEGS during the scheduling period The set of baseline state variables within; For random scenarios Next scheduling period Internal IEGS in direction Safety margin; For scheduling period Internal IEGS in direction Robust safety margin, i.e. Each running point within can be used by any random scenario. Down Included; Therefore, the above two equations can be rewritten as: ； ； In the formula: and Distributed to scheduling periods Internal IEGS in direction Robust upper boundary point and robust lower boundary point; and Random scenes Next scheduling period Internal IEGS in direction The upper and lower boundary points.

6. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy, as described in claim 4, is characterized in that: The optimization problem of reducing the safety region in a high-dimensional space to a one-dimensional space by using the weight coefficient allocation method is achieved through the following optimization solution model: ； ； In the formula, For scheduling period Internal IEGS in random scenarios Global security margin; For scheduling period Global robust safety margin of internal IEGS; By adjusting the direction of energy injection into higher dimensions, the above two equations can be rewritten as: ； ； In the formula, and Distributed to scheduling periods Robust upper and lower boundary points of the inner IEGS; and Distributed to scheduling periods Internal IEGS in random scenarios The upper and lower boundary points in the equation.

7. A robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy, as described in any one of claims 1-6, characterized in that: The robust boundary points for each scheduling period are solved by the radial orbit sampling method. The parameters involved include the structural topology and equipment parameters of the integrated electrical energy system, the maximum orbit rotation coefficient, the operating cycle, and the initial energy flow distribution state of the integrated electrical energy system.

8. The robust security domain analysis method for an integrated electrical energy system considering the uncertainty of renewable energy sources according to claim 7, characterized in that: Renewable energy sources include wind power and solar power.

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