Improved affine arithmetic based on spatiotemporal correlation for distribution network branch power flow analysis

Abstract

This invention discloses a distribution network interval power flow analysis method based on improved affine arithmetic with spatiotemporal correlation. The method includes: establishing a basic distribution network model; constructing a comprehensive sensitivity index to partition the distribution network; establishing a spatiotemporal correlated multi-noise affine model; constructing improved affine arithmetic rules based on the spatiotemporal correlated multi-noise affine model; establishing a mapping relationship between node current disturbances and node voltage disturbances, and substituting the spatiotemporal correlated multi-noise affine model to obtain the affine expressions for node voltage and branch power flow; estimating the upper bound of the nonlinear residual term in power flow propagation, and introducing an auxiliary residual noise term for bounded encapsulation to obtain the interval results for the voltage amplitude, phase angle, and branch power flow of each node. This invention overcomes the deficiency of current distribution network interval power flow analysis that ignores the spatiotemporal correlation characteristics of uncertainty, while improving computational accuracy and solution efficiency, providing theoretical support for subsequent distribution network security assessment.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to distribution network operation evaluation technology, specifically to a distribution network interval power flow analysis method based on improved affine arithmetic with spatiotemporal correlation. Background Technology

[0002] With the large-scale integration of distributed power sources such as wind and solar power into the distribution network, the power output and randomness of the system are constantly increasing, and the operating state of the distribution network exhibits significant uncertainty. Traditional power flow analysis methods are usually based on deterministic operating conditions to build models, which makes it difficult to accurately reflect the propagation process of distributed power source disturbances in the network, and also difficult to effectively describe the range of changes in state variables such as node voltage and phase angle under uncertain conditions.

[0003] Existing methods for analyzing uncertain power flows mainly include fuzzy methods, probabilistic methods, and interval methods. Among them, interval methods, because they only require the upper and lower boundaries of uncertain variables, are more suitable for distribution network scenarios where historical samples are insufficient or probability distributions are difficult to obtain accurately. In recent years, affine arithmetic has been introduced into interval power flow analysis to preserve the correlation between uncertain variables and reduce the conservatism of traditional interval methods. However, existing technologies still do not adequately characterize the spatiotemporal correlation structure of input uncertainties in distributed power sources such as wind power and photovoltaics. Furthermore, during the nonlinear propagation of power flows, affine arithmetic easily introduces additional noise terms, leading to interval expansion, wider boundaries, and increased computational burden. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing power flow analysis methods for distribution networks in characterizing the spatiotemporal correlation structure of uncertainties in the input of distributed power sources such as wind power and photovoltaics, and the problems that affine arithmetic easily introduces additional noise terms during the nonlinear propagation of power flow, leading to interval expansion, conservative boundaries, and increased computational burden, this invention provides a power flow analysis method for distribution networks based on improved affine arithmetic with spatiotemporal correlation. This method effectively characterizes regional shared disturbances and local node disturbances, and suppresses noise growth caused by nonlinear propagation while ensuring interval coverage, thereby improving the compactness, stability, and computational efficiency of the power flow results for distribution networks.

[0005] Technical Solution: To achieve the above objectives, this invention provides a power flow analysis method for distribution network sections based on improved affine arithmetic with spatiotemporal correlation, comprising the following steps:

[0006] S1: Obtain the network topology, node parameters, branch parameters, distributed power source access information, and load data of the distribution network to establish a basic model of the distribution network;

[0007] S2: Based on the basic model of the distribution network, a comprehensive sensitivity index is constructed based on the power flow linearization results of the distribution network at the operating point. The electrical distance between nodes is calculated to construct the expected electrical distance matrix of the distribution network. The distribution network is then partitioned in multiple typical scenarios using the attractor propagation clustering algorithm.

[0008] S3: For the prediction error sequence of distributed power sources in each zone of the distribution network, combined with spatial correlation analysis, time lag estimation and principal component analysis, the uncertainty injection is decomposed into regional shared noise term and node local noise term, and a spatiotemporal correlated multi-noise affine model is established.

[0009] S4: An improved affine arithmetic rule is constructed based on a spatiotemporally correlated multi-noise affine model. The rule preserves the inheritance of noise sets for linear arithmetic operations, adopts an interval Taylor first-order approximation for reciprocal operations, and encapsulates the linear dominant term and second-order coupled residual for multiplication operations.

[0010] S5: Linearize the power flow equations near the deterministic operating point, establish the mapping relationship between node current disturbances and node voltage disturbances, and substitute the spatiotemporally correlated multi-noise affine model to obtain the affine expressions of node voltage and branch power flow.

[0011] S6: Estimate the upper bound of the nonlinear residual term in the power flow propagation and introduce an auxiliary residual noise term for bounded encapsulation to obtain the interval results of the voltage amplitude, phase angle and branch power flow of each node.

[0012] Further, step S1 includes:

[0013] A1: Obtain the network topology and line impedance parameters of the distribution network, and construct the network admittance matrix;

[0014] A2: Based on the given active and reactive power injection information of the nodes, the reference bus settings and the per-unit benchmark, determine the deterministic operating point of the distribution network;

[0015] A3: Based on the distributed power source prediction interval, prediction error sequence, and load data, uncertainty modeling input parameters are formed. The uncertainty modeling input parameters include the noise set and coefficients corresponding to regional shared disturbances and node local disturbances, interval boundaries, and the upper bound estimation rules and residual noise settings required for nonlinear residual encapsulation.

[0016] Further, step S2 includes:

[0017] B1: Based on the power flow Jacobian matrix, establish the sensitivity relationship between node voltage and node active and reactive power injection to construct a comprehensive sensitivity index. The specific steps are as follows:

[0018] B1-1: The power flow linearization of a distribution network at a certain operating point is expressed as:

[0019]

[0020] in, , These represent the node voltage magnitude and phase angle, respectively. , These represent the active and reactive power injections of the node, respectively. The current Jacobian matrix is ​​the inverse matrix of the current Jacobian matrix. The sensitivity of node voltage to power injection disturbances can be obtained directly; This represents the active power disturbance. This represents the reactive power disturbance. This represents the node voltage phase angle increment. This represents the increment of the node voltage amplitude.

[0021] B1-2: Based on the linearized expression of power flow in the distribution network, considering the deviation caused by the sensitivity in one direction between two nodes, a sensitivity difference index is proposed with the node's own voltage response to its own injection as the benchmark:

[0022]

[0023] in, Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-reactive power sensitivity; Represents the node Its own voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; For nodes With nodes The difference in active sensitivity between them For nodes With nodes The reactive power sensitivity difference index between them;

[0024] B1-3: Considering the different contribution ratios of active and reactive power to voltage, construct a comprehensive sensitivity index. :

[0025]

[0026] Among them, the weighting coefficient Define as a node The ratio of the voltage change generated by active power to the total voltage change generated by power;

[0027] B2: Construct the expected electrical distance matrix of the distribution network;

[0028] For the comprehensive sensitivity matrix Normalization and logarithmic transformation are performed:

[0029]

[0030] in, For nodes With nodes The normalized value of the overall sensitivity compresses all the overall sensitivities to a similar scale. For point With nodes The logarithm of the overall sensitivity is taken after normalization to improve the numerical discrimination.

[0031] Then the node The coupling relationships of other nodes in the entire network are represented by vectors. The electrical distance between nodes is defined by the Euclidean norm between the coupling feature vectors of two nodes. Considering the fluctuations in distributed power generation output, the distributed power generation output data is grouped into sample vectors according to time periods, and K-means clustering is performed based on Euclidean distance. A typical scenario, among which The probability of occurrence is Calculate the electrical distance matrix in each scenario. The final electrical distance expectation matrix of the distribution network Represented as:

[0032]

[0033] in, Indicates the typical operating scenario number; This represents the total number of typical scenarios;

[0034] B3: Attractor propagation clustering is used to determine partition centers and partitioning results;

[0035] The obtained electrical distance expectation matrix is ​​transformed into a similarity matrix, and then... The responsibility is updated iteratively using AP clustering. and availability :

[0036]

[0037]

[0038] in, Candidate nodes As a node The suitability of the representative points; For similarity OK Column elements; For similarity OK Column elements; For nodes The suitability of itself as a candidate cluster center; For nodes More suitable as a node compared to other candidate points The degree of representation;

[0039] Introducing damping coefficient Perform smooth updates to responsibility and availability:

[0040]

[0041]

[0042] in, The first one is calculated by the original update formula of responsibility. Updated value of the second candidate's responsibility. For the process After the second iteration, the node For candidate representative points Degree of responsibility The first value calculated by the original availability update formula. Secondary candidate availability update value For the process After the second iteration, the node For candidate representative points Availability; For the process After the second iteration, the node For candidate representative points Smoothly update the responsibility level value; For the process After the second iteration, the node For candidate representative points Availability is updated smoothly;

[0043] For any node ,go through After convergence of the last iteration, choose to make and The node whose sum reaches its maximum value As a node The representative point, if Then node If a node is selected as the cluster center, then nodes with the same representative point are grouped into the same cluster to obtain the final partitioning result.

[0044] Furthermore, the process of establishing the spatiotemporally correlated multi-noise affine model in step S3 includes:

[0045] C1: Perform interval predictions for photovoltaic and wind power units respectively, obtain the output prediction intervals of each distributed power source at each time, and calculate the corresponding prediction error sequences respectively;

[0046] C2: Perform spatial correlation analysis and time shift correlation analysis on the prediction error sequence of distributed power sources in the same region to extract the spatial correlation and dominant time delay relationship between distributed power sources in the region;

[0047] C3: Construct a covariance matrix based on the prediction error matrix within the region and perform principal component decomposition to extract the dominant shared disturbance mode, obtain the sharing degree of each distributed power source, and determine the regional shared noise figure and node local noise figure according to the interval consistency constraint.

[0048] C4: Based on the interval prediction results, regional shared noise coefficient and node local noise coefficient, a spatiotemporal correlation multi-noise affine model of node distributed power output is established.

[0049] Further, step C2 includes:

[0050] C2-1: Construct a spatial correlation matrix for the uncertainty of distributed power output and quantify the spatial correlation between different units;

[0051] set up At this moment, node Prediction error of distributed power generation output Represented as:

[0052]

[0053] in, For nodes The actual output of the distributed power source; This corresponds to the center value of the predicted power;

[0054] Calculate the Pearson correlation coefficient between any two distributed generation units, and construct the spatial correlation matrix of photovoltaic output uncertainty, as expressed by:

[0055]

[0056] in, The spatial correlation matrix, for Time node The prediction error of distributed power generation output for Time node Prediction error of distributed power generation output;

[0057] C2-2: A time-delay estimation method based on cross-correlation alignment extracts the dominant lag relationship of error fluctuations at different nodes from historical prediction error sequences to quantify time correlation;

[0058] For any two nodes in the distribution network system , Cross-correlation function Defined as:

[0059]

[0060] in, In order to be in node at time +S The error sequence, In order to be in Time node The error sequence; The time shift step size; when At that time, node Error sequence relative to nodes Lag One time step, otherwise it is ahead;

[0061] By traversing a finite time offset range To obtain the optimal time offset as follows:

[0062]

[0063] The cross-correlation is normalized, and a time-form consistency index is defined. for:

[0064]

[0065] in, and They are nodes , The autocorrelation term, and The larger the absolute value, the more significant its time correlation.

[0066] Further, step C3 includes:

[0067] C3-1: Calculate the degree of uncertainty in shared resources

[0068] Suppose a certain AP partition Contains The prediction error matrix of a photovoltaic unit within the time window T is expressed as:

[0069]

[0070] in, , These represent the first distributed power source in , The prediction error at any given time; , These represent the second distributed power source in , The prediction error at any given time; , The first A distributed power source in , The prediction error at any given time; For the first Distributed power output prediction error matrix within each partition;

[0071] Construct on this basis Covariance matrix of distributed generation prediction error within each partition:

[0072]

[0073] in, This represents the number of sampling points within the time window.

[0074] right Eigenvalue decomposition yields:

[0075]

[0076] in, For the first The eigenvector matrix of each partition represents the shared perturbation direction. For the first The eigenvalue diagonal matrix of each partition represents the importance of each perturbation direction;

[0077] Define nodes based on the above formulas. Uncertainty sharing index for:

[0078]

[0079] Among them, eigenvalues satisfy ; The largest eigenvalue of the covariance matrix The corresponding eigenvector of the first 1 element, and , ; for The prediction error covariance matrix within each partition is the first... 1 eigenvalue, Indicates the number of distributed power sources participating in the modeling within the partition;

[0080] C3-2: Extracting shared noise figure and local noise figure

[0081] exist At time t, the interval prediction yields the node. Output power range The center value and half width of the interval are specifically represented as follows:

[0082]

[0083] in, For nodes At any moment The center value of the distributed power generation output prediction interval, For nodes At any moment The half-width of the output prediction interval for distributed power sources For nodes exist The lower bound of the prediction interval is given at any given time. For nodes exist The upper bound of the time prediction interval;

[0084] Based on the above formula, apply interval consistency constraints to the affine coefficients:

[0085]

[0086]

[0087]

[0088] in, , These are the affine coefficients corresponding to shared and local uncertainties, respectively.

[0089] Further, step S4 includes:

[0090] D1: The obtained multi-noise affine output of the distributed power source is uniformly expressed in the form of complex power;

[0091] For nodes ,exist Complex power expression at time t for:

[0092]

[0093] in, These are deterministic predicted values; Includes shared noise and local noise;

[0094] D2: For deterministic linear operations, keep the input noise set unchanged and do not introduce new noise symbols;

[0095] D3: For reciprocal or division operations, under the condition of non-singularity, a first-order affine approximation based on interval Taylor expansion is used to construct the reciprocal expression, and a higher-order residual noise term is introduced to cover higher-order nonlinear errors.

[0096] By the definition of affine arithmetic, we can assume:

[0097]

[0098] in, For deterministic components, For affine perturbation terms, for Consider the affine representation of the state variables under uncertainty at any given time, and satisfy the non-singular condition:

[0099]

[0100] in, for At this moment The affine coefficients corresponding to each noise element Describing affine variables The radius;

[0101] Then the function In the interval The above is represented as:

[0102]

[0103] in, The higher-order nonlinear residual noise element generated by Taylor expansion is used to cover higher-order nonlinear errors; The coefficient of the remainder term;

[0104] D4: For the multiplication of two complex affine variables that share the same noise set, decompose them into linear dominant terms and second-order coupled terms, and encapsulate the second-order coupled terms as bounded residuals in a unified manner.

[0105] The specific expression is:

[0106]

[0107] in, , Representing time respectively The first unified spatiotemporal correlated noise set The and the first One affine noise element; For a moment The first uncertain variable containing spatiotemporal correlation noise, For a moment The second uncertainty variable includes spatiotemporal correlation noise. for The deterministic central value, for The deterministic central value, for The The affine coefficients corresponding to each noise element for The Middle Affine coefficients corresponding to each noise element;

[0108] The linear dominant term is retained as the main source of uncertainty, while the second-order coupled terms are uniformly treated as bounded residuals and covered by a single residual noise, i.e.:

[0109]

[0110] in, For the reason and The given upper bound estimate, This is a newly added residual noise element.

[0111] Further, step S5 includes:

[0112] E1: Ignore uncertain disturbance terms and perform power flow calculations only on deterministic power injection to obtain the deterministic operating point voltage;

[0113] E2: The uncertain node voltage is expressed as the sum of the deterministic component and the disturbance component, and the node current injection relationship is expanded in the vicinity of the deterministic operating point. The voltage disturbance is decomposed into a linear dominant term and a nonlinear residual term.

[0114] E3: An approximate expression for nodal current injection is constructed based on the first-order expansion result, wherein the denominators of the division operations involved in the expansion process are all deterministic complex numbers;

[0115] E4: By utilizing the relationship between network current and voltage, current disturbances are mapped to node voltage disturbances to obtain affine expressions for node voltage disturbances, and further, affine expressions for branch power flows are obtained.

[0116] Further, step S6 includes:

[0117] F1: Estimate the upper bound of the nonlinear residual term and introduce an auxiliary residual noise term to over-approximate the nonlinear residual term;

[0118] F2: Substitute the encapsulated residual terms back into the node voltage perturbation mapping relationship to obtain the final affine expression of the node voltage;

[0119] F3: Calculate the voltage amplitude range of each node, the voltage phase angle range of each node, and the power flow range of each branch based on the final affine expression.

[0120] Beneficial Effects: Compared with existing technologies, this invention, by constructing a distribution network partitioning method based on comprehensive sensitivity electrical distance and attractor propagation clustering, can extract regional shared disturbances at the structural level; by decomposing distributed generation uncertainty injection into regional shared noise and node local noise, and establishing a multi-noise spatiotemporal affine model, it can more accurately characterize the spatiotemporal correlation features of wind power and photovoltaic output uncertainty; by adopting interval Taylor first-order approximation and residual encapsulation strategies to improve the affine arithmetic rules, it can effectively control the number of new noise terms and suppress interval expansion while ensuring interval solution coverage; therefore, this invention can obtain more compact interval power flow results and improve the efficiency and stability of large-scale distribution network interval power flow calculation, providing effective technical support for distribution network operation monitoring, analysis and control under high proportion of distributed generation access conditions. Attached Figure Description

[0121] Figure 1 This is a schematic flowchart of the method of the present invention;

[0122] Figure 2 Forecast interval diagram of wind turbine units;

[0123] Figure 3 Heat map of wind turbine prediction error;

[0124] Figure 4 Forecast interval diagram of photovoltaic modules;

[0125] Figure 5 Heatmap of photovoltaic module prediction error;

[0126] Figure 6 A comparison chart of node voltage amplitudes for different algorithms;

[0127] Figure 7 A comparison chart of node voltage angles for different algorithms;

[0128] Figure 8 This chart compares the degree of improvement of different algorithms. Detailed Implementation

[0129] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0130] Example 1:

[0131] like Figure 1 As shown, this embodiment provides a power flow analysis method for distribution network sections based on improved affine arithmetic with spatiotemporal correlation, including the following steps:

[0132] S1: Obtain the network topology, node parameters, branch parameters, distributed power source access information, and load data of the distribution network to establish a basic model of the distribution network;

[0133] Step S1 includes:

[0134] A1: Obtain the network topology and line impedance parameters of the distribution network, and construct the network admittance matrix;

[0135] A2: Based on the given active and reactive power injection information of the nodes, the reference bus settings and the per-unit benchmark, determine the deterministic operating point of the distribution network;

[0136] A3: Based on the distributed power source prediction interval, prediction error sequence, and load data, uncertainty modeling input parameters are formed. The uncertainty modeling input parameters include the noise set and coefficients corresponding to regional shared disturbances and node local disturbances, interval boundaries, and the upper bound estimation rules and residual noise settings required for nonlinear residual encapsulation.

[0137] In this embodiment, three wind power units with a rated capacity of 400kW are connected to nodes 16, 21 and 32 of the IEEE33 system, and six photovoltaic units with a rated capacity of 200kW are connected to nodes 6, 14, 16, 18, 24, 30 and 33. The system reference voltage is set to 12.66kV and the reference power is 10MW.

[0138] S2: Based on the basic model of the distribution network, a comprehensive sensitivity index is constructed based on the power flow linearization results of the distribution network at the operating point. The electrical distance between nodes is calculated to construct the expected electrical distance matrix of the distribution network. The distribution network is then partitioned in multiple typical scenarios using the attractor propagation clustering algorithm.

[0139] Step S2 includes:

[0140] B1: Based on the power flow Jacobian matrix, establish the sensitivity relationship between node voltage and node active and reactive power injection to construct a comprehensive sensitivity index. The specific steps are as follows:

[0141] B1-1: The power flow linearization of a distribution network at a certain operating point is expressed as:

[0142]

[0143] in, , These represent the node voltage magnitude and phase angle, respectively. , These represent the active and reactive power injections of the node, respectively. The current Jacobian matrix is ​​the inverse matrix of the current Jacobian matrix. The sensitivity of node voltage to power injection disturbances can be obtained directly; This represents the active power disturbance. This represents the reactive power disturbance. This represents the node voltage phase angle increment. This represents the increment of the node voltage amplitude.

[0144] B1-2: Based on the linearized expression of power flow in the distribution network, considering the deviation caused by the sensitivity in one direction between two nodes, a sensitivity difference index is proposed with the node's own voltage response to its own injection as the benchmark:

[0145]

[0146] in, Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-reactive power sensitivity; Represents the node Its own voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; For nodes With nodes The difference in active sensitivity between them For nodes With nodes The reactive power sensitivity difference index between them;

[0147] B1-3: Considering the different contribution ratios of active and reactive power to voltage, construct a comprehensive sensitivity index. :

[0148]

[0149] Among them, the weighting coefficient Define as a node The ratio of the voltage change generated by active power to the total voltage change generated by power;

[0150] B2: Construct the expected electrical distance matrix of the distribution network;

[0151] For the comprehensive sensitivity matrix Normalization and logarithmic transformation are performed:

[0152]

[0153] in, For nodes With nodes The normalized value of the overall sensitivity compresses all the overall sensitivities to a similar scale. For point With nodes The logarithm of the overall sensitivity is taken after normalization to improve the numerical discrimination.

[0154] Then the node The coupling relationships of other nodes in the entire network are represented by vectors. The electrical distance between nodes is defined by the Euclidean norm between the coupling feature vectors of two nodes. Considering the fluctuations in distributed power generation output, the distributed power generation output data is grouped into sample vectors according to time periods, and K-means clustering is performed based on Euclidean distance. A typical scenario, among which The probability of occurrence is Calculate the electrical distance matrix in each scenario. The final electrical distance expectation matrix of the distribution network Represented as:

[0155]

[0156] in, Indicates the typical operating scenario number; This represents the total number of typical scenarios;

[0157] B3: Attractor propagation clustering is used to determine partition centers and partitioning results;

[0158] The obtained electrical distance expectation matrix is ​​transformed into a similarity matrix, and then... The responsibility is updated iteratively using AP clustering. and availability :

[0159]

[0160]

[0161] in, Candidate nodes As a node The suitability of the representative points; For similarity OK Column elements; For similarity OK Column elements; For nodes The suitability of itself as a candidate cluster center; For nodes More suitable as a node compared to other candidate points The degree of representation;

[0162] Introducing damping coefficient Perform smooth updates to responsibility and availability:

[0163]

[0164] in, The first one is calculated by the original update formula of responsibility. Updated value of the second candidate's responsibility. For the process After the second iteration, the node For candidate representative points Degree of responsibility The first value calculated by the original availability update formula. Secondary candidate availability update value For the process After the second iteration, the node For candidate representative points Availability; For the process After the second iteration, the node For candidate representative points Smoothly update the responsibility level value; For the process After the second iteration, the node For candidate representative points Availability is updated smoothly;

[0165] For any node ,go through After convergence of the last iteration, choose to make and The node whose sum reaches its maximum value As a node The representative point, if Then node If a node is selected as the cluster center, then nodes with the same representative point are grouped into the same cluster to obtain the final partitioning result.

[0166] Finally, to ensure consistency between the partitioning results and the physical structure of the distribution network and the subsequent shared noise mapping, the following constraints are imposed on the candidate partitions: the subgraph corresponding to each region must be connected; each region must contain at least one DG access node to ensure that the regional shared noise can be mapped to the uncertainty of actual injection; and avoid forming too small regions that would distort the noise sharing assumption.

[0167] S3: For the prediction error sequence of distributed power sources in each zone of the distribution network, combined with spatial correlation analysis, time lag estimation and principal component analysis, the uncertainty injection is decomposed into regional shared noise term and node local noise term, and a spatiotemporal correlated multi-noise affine model is established.

[0168] The process of establishing a spatiotemporally correlated multi-noise affine model includes:

[0169] C1: Perform interval predictions for photovoltaic and wind power units respectively, obtain the output prediction intervals of each distributed power source at each time, and calculate the corresponding prediction error sequences respectively;

[0170] C2: Perform spatial correlation analysis and time shift correlation analysis on the prediction error sequence of distributed power sources in the same region to extract the spatial correlation and dominant time delay relationship between distributed power sources in the region;

[0171] Step C2 includes:

[0172] C2-1: Construct a spatial correlation matrix for the uncertainty of distributed power output and quantify the spatial correlation between different units;

[0173] set up At this moment, node Prediction error of distributed power generation output Represented as:

[0174]

[0175] in, For nodes The actual output of the distributed power source; This corresponds to the center value of the predicted power;

[0176] Calculate the Pearson correlation coefficient between any two distributed generation units, and construct the spatial correlation matrix of photovoltaic output uncertainty, as expressed by:

[0177]

[0178] in, The spatial correlation matrix, for Time node The prediction error of distributed power generation output for Time node Prediction error of distributed power generation output;

[0179] C2-2: A time-delay estimation method based on cross-correlation alignment extracts the dominant lag relationship of error fluctuations at different nodes from historical prediction error sequences to quantify time correlation;

[0180] For any two nodes in the distribution network system , Cross-correlation function Defined as:

[0181]

[0182] in, In order to be in node at time +S The error sequence, In order to be in Time node The error sequence; The time shift step size; when At that time, node Error sequence relative to nodes Lag One time step, otherwise it is ahead;

[0183] By traversing a finite time offset range To obtain the optimal time offset as follows:

[0184]

[0185] The cross-correlation is normalized, and a time-form consistency index is defined. for:

[0186]

[0187] in, and They are nodes , The autocorrelation term, and The larger the absolute value, the more significant its time correlation.

[0188] C3: Construct a covariance matrix based on the prediction error matrix within the region and perform principal component decomposition to extract the dominant shared disturbance mode, obtain the sharing degree of each distributed power source, and determine the regional shared noise figure and node local noise figure according to the interval consistency constraint.

[0189] Step C3 includes:

[0190] C3-1: Calculate the degree of uncertainty in shared resources

[0191] Suppose a certain AP partition Contains The prediction error matrix of a photovoltaic unit within the time window T is expressed as:

[0192]

[0193] in, , These represent the first distributed power source in , The prediction error at any given time; , These represent the second distributed power source in , The prediction error at any given time; , The first A distributed power source in , The prediction error at any given time; For the first Distributed power output prediction error matrix within each partition;

[0194] Construct on this basis Covariance matrix of distributed generation prediction error within each partition :

[0195]

[0196] in, This represents the number of sampling points within the time window.

[0197] right Eigenvalue decomposition yields:

[0198]

[0199] in, For the first The eigenvector matrix of each partition represents the shared perturbation direction. For the first The eigenvalue diagonal matrix of each partition represents the importance of each perturbation direction;

[0200] Define nodes based on the above formulas. Uncertainty sharing index for:

[0201]

[0202] Among them, eigenvalues satisfy ; The largest eigenvalue of the covariance matrix The corresponding eigenvector of the first 1 element, and , ; for The prediction error covariance matrix within each partition is the first... 1 eigenvalue, Indicates the number of distributed power sources participating in the modeling within the partition;

[0203] C3-2: Extracting shared noise figure and local noise figure

[0204] exist At time t, the interval prediction yields the node. Output power range The center value and half width of the interval are specifically represented as follows:

[0205]

[0206] in, For nodes At any moment The center value of the distributed power generation output prediction interval, For nodes At any moment The half-width of the output prediction interval for distributed power sources For nodes exist The lower bound of the prediction interval is given at any given time. For nodes exist The upper bound of the time prediction interval;

[0207] Based on the above formula, apply interval consistency constraints to the affine coefficients:

[0208]

[0209]

[0210]

[0211] in, , These are the affine coefficients corresponding to shared and local uncertainties, respectively.

[0212] C4: Based on interval prediction results, regional shared noise figure, and node local noise figure, establish a spatiotemporal correlation multi-noise affine model for node distributed power output. Its expression is as follows:

[0213]

[0214] in, This represents the regional sharing uncertainty noise of distributed power sources; Represents the node at time t The local uncertainty noise at the location is between -1 and 1.

[0215] In this embodiment, wind power prediction uses a spatiotemporal quantile regression algorithm; photovoltaic prediction uses a prediction model based on two-level decomposition and WOA-BiLSTM-Attention. The prediction results for 96 time points throughout May 20, 2018, are selected as representative examples, with a confidence level of 95%. The power range predictions for wind power and photovoltaics are as follows: Figure 2 and Figure 4 As shown.

[0216] In this embodiment, wind power errors are calculated using an error sequence over 24 time periods, and the Pearson correlation coefficient is determined. For photovoltaic (PV) units, error sequences for each unit are constructed within a 24-hour overall time window, and a correlation coefficient matrix is ​​obtained. Furthermore, to eliminate the impact of differences in installed capacity, the power sequences for each site are normalized to a per-unit sequence based on the maximum available power of the sample. Interval predictions, error sequences, and correlation matrices are all calculated based on the per-unit sequences. The thermodynamics of prediction errors for wind power and PV are as follows: Figure 3 and Figure 5 As shown.

[0217] S4: Based on the spatiotemporal correlation multi-noise affine model, an improved affine arithmetic rule is constructed. The noise set inheritance is maintained for linear arithmetic operations, the interval Taylor first-order approximation is adopted for the reciprocal operation, and the linear dominant term and the second-order coupled residual are separated and encapsulated for the multiplication operation.

[0218] Step S4 includes:

[0219] D1: The obtained multi-noise affine output of the distributed power source is uniformly expressed in the form of complex power;

[0220] For nodes ,exist Complex power at time t Expressed as:

[0221]

[0222] in, These are deterministic predicted values; Includes shared noise and local noise;

[0223] D2: For deterministic linear operations such as scalar multiplication, matrix multiplication, and addition and subtraction, the input noise set remains unchanged, and no new noise symbols are introduced;

[0224] D3: For reciprocal or division operations, under the condition of non-singularity, a first-order affine approximation based on interval Taylor expansion is used to construct the reciprocal expression, and a higher-order residual noise term is introduced to cover higher-order nonlinear errors.

[0225] By the definition of affine arithmetic, we can assume:

[0226]

[0227] in, For deterministic components, For affine perturbation terms, for Consider the affine representation of the state variables under uncertainty at any given time, and satisfy the non-singular condition:

[0228]

[0229] in, for At this moment The affine coefficients corresponding to each noise element Describing affine variables The radius;

[0230] Then the function In the interval The above is represented as:

[0231]

[0232] in, The higher-order nonlinear residual noise element generated by Taylor expansion is used to cover higher-order nonlinear errors; The coefficient of the remainder term can be conservatively estimated using interval information;

[0233] D4: For the multiplication of two complex affine variables that share the same noise set, decompose them into linear dominant terms and second-order coupled terms, and encapsulate the second-order coupled terms as bounded residuals in a unified manner.

[0234] The specific expression is:

[0235]

[0236] in, , Representing time respectively The first unified spatiotemporal correlated noise set The and the first One affine noise element; For a moment The first uncertain variable containing spatiotemporal correlation noise, For a moment The second uncertainty variable includes spatiotemporal correlation noise. for The deterministic central value, for The deterministic central value, for The The affine coefficients corresponding to each noise element for The Middle The affine coefficients corresponding to each noise element. If affine propagation is performed term by term for the second-order coupled terms, the amount of noise will increase significantly. At the arithmetic level, a staged processing strategy is adopted: the linear dominant term is retained as the main source of uncertainty, while the second-order coupled terms are uniformly treated as bounded residuals and covered by a single residual noise, i.e.:

[0237]

[0238] in, For the reason and The given upper bound estimate, This is a newly added residual noise element.

[0239] S5: Linearize the power flow equations near the deterministic operating point, establish the mapping relationship between node current disturbances and node voltage disturbances, and substitute the spatiotemporally correlated multi-noise affine model to obtain the affine expressions of node voltage and branch power flow.

[0240] Step S5 includes:

[0241] E1: Ignore uncertain disturbance terms and perform power flow calculations only on deterministic power injection to obtain the deterministic operating point voltage;

[0242]

[0243] in, Represents a node At any moment Deterministic complex power injection; Represents a node At any moment The deterministic operating point voltage; Represents the elements in the nodal admittance matrix; Represents a node At any moment The deterministic operating point voltage;

[0244] E2: The uncertain node voltage is expressed as the sum of the deterministic component and the disturbance component, and the node current injection relationship is expanded in the vicinity of the deterministic operating point. The voltage disturbance is decomposed into a linear dominant term and a nonlinear residual term.

[0245]

[0246] in, Represents a node At any moment Uncertain node voltages; This represents the amount of node voltage disturbance;

[0247]

[0248] in, Represents a node At any moment The amount of current disturbance; This represents the linear dominant term obtained from the first-order expansion; This represents the nonlinear residual term retained after truncation of the first-order expansion;

[0249] E3: An approximate expression for nodal current injection is constructed based on the first-order expansion result, wherein the denominators of the division operations involved in the expansion process are all deterministic complex numbers;

[0250]

[0251] in, Represents a node At any moment The complex power injection disturbance; The conjugate of the deterministic operating point voltage; Represents the conjugate of deterministic complex power injection; The conjugate of the node voltage disturbance; Represents a node At any moment The first-order linear approximation of the current injection disturbance;

[0252] E4: By utilizing the relationship between network current and voltage, the current disturbance is mapped to the node voltage disturbance to obtain the affine expression of the node voltage disturbance, and further, the affine expression of the branch power flow is obtained.

[0253]

[0254] in, Indicates at time The voltage perturbation vector of all nodes; Indicates at time The current perturbation vector of all nodes; This represents the nodal admittance matrix.

[0255] S6: Estimate the upper bound of the nonlinear residual term in the power flow propagation and introduce an auxiliary residual noise term for bounded encapsulation to obtain the interval results of the voltage amplitude, phase angle and branch power flow of each node.

[0256] Step S6 includes:

[0257] F1: Estimate the upper bound of the nonlinear residual term and introduce an auxiliary residual noise term to over-approximate the nonlinear residual term;

[0258]

[0259] in, For residual terms The upper bound radius, To assist in the residual noise term;

[0260] F2: Substitute the encapsulated residual terms back into the node voltage perturbation mapping relationship to obtain the final affine expression of the node voltage;

[0261]

[0262] in, For nodes At any moment The final affine voltage expression, For the node voltage at the deterministic operating point, For the nodal voltage perturbation affine term obtained by uncertain injection propagation;

[0263] F3: Calculate the voltage amplitude range and voltage phase angle range of each node based on the final affine expression, as follows:

[0264]

[0265]

[0266] in, , Representing nodes respectively At any moment The lower and upper bounds of the node voltage amplitude; , Representing nodes respectively At any moment The lower and upper bounds of the node voltage phase angle; Represents a node At any moment The deterministic operating point voltage amplitude; Represents a node At any moment The deterministic operating point voltage phase angle; Represents a node At any moment The final expression for the affine voltage; Represents affine voltage variable The disturbance radius.

[0267] The method of this invention makes up for the shortcomings of current power flow analysis of distribution network sections that ignores the spatiotemporal correlation characteristics of uncertainty, while improving the calculation accuracy and solution efficiency, and providing theoretical support for subsequent distribution network security assessment.

[0268] Example 2:

[0269] To verify the effectiveness and efficacy of the method of the present invention, the following simulation experiments and data analysis were conducted in this embodiment:

[0270] The simulation results of STC-IA, STC-AA, and Monte Carlo MC were compared, and algorithm improvement indicators were introduced. :

[0271]

[0272] in, , STC-AA at nodes The upper and lower bound voltages at the point; , For STC-IA at the node The upper and lower bound voltages at the point.

[0273] like Figure 6 As shown, the results of different algorithms for solving the node voltage amplitude range in the improved IEEE 33-node distribution system are presented. Both the method of this invention and the comparative method can form an effective envelope of the Monte Carlo benchmark results, but the interval boundary obtained by the method of this invention is closer to the benchmark results, and the interval redundancy is smaller. This indicates that the method of this invention can effectively reduce the conservatism of the node voltage amplitude range while ensuring interval coverage, and improve the compactness of the results and the estimation accuracy.

[0274] like Figure 7 As shown, the results of different algorithms for solving the phase angle interval of node voltage in the improved IEEE 33-node distribution system are presented. The method of this invention can obtain the phase angle interval envelope with high consistency with the Monte Carlo results at each node, and has a smaller interval expansion compared with the comparison method. This indicates that the method of this invention also has good interval control capability and stability for the phase angle, a state variable that is highly sensitive to nonlinear propagation.

[0275] like Figure 8 As shown, the results are calculated based on the voltage interval boundaries of each time period and node throughout the 24-hour period, and are used to characterize the degree of improvement of the method of the present invention in terms of interval compactness compared with the comparative method. The method of the present invention shows a positive improvement in most nodes and time periods, indicating that the method of the present invention can systematically reduce the width of the node voltage interval and reduce the conservatism of the results while ensuring interval coverage, and maintain a stable accuracy advantage under multi-condition operation throughout the day.

Claims

1. A distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation, characterized in that, Includes the following steps: S1: Obtain the network topology, node parameters, branch parameters, distributed power source access information, and load data of the distribution network to establish a basic model of the distribution network; S2: Based on the basic model of the distribution network, a comprehensive sensitivity index is constructed based on the power flow linearization results of the distribution network at the operating point. The electrical distance between nodes is calculated to construct the expected electrical distance matrix of the distribution network. The distribution network is then partitioned in multiple typical scenarios using the attractor propagation clustering algorithm. S3: For the prediction error sequence of distributed power sources in each zone of the distribution network, combined with spatial correlation analysis, time lag estimation and principal component analysis, the uncertainty injection is decomposed into regional shared noise term and node local noise term, and a spatiotemporal correlated multi-noise affine model is established. S4: An improved affine arithmetic rule is constructed based on a spatiotemporally correlated multi-noise affine model. The rule preserves the inheritance of noise sets for linear arithmetic operations, adopts an interval Taylor first-order approximation for reciprocal operations, and encapsulates the linear dominant term and second-order coupled residual for multiplication operations. S5: Linearize the power flow equations near the deterministic operating point, establish the mapping relationship between node current disturbances and node voltage disturbances, and substitute the spatiotemporally correlated multi-noise affine model to obtain the affine expressions of node voltage and branch power flow. S6: Estimate the upper bound of the nonlinear residual term in the power flow propagation and introduce an auxiliary residual noise term for bounded encapsulation to obtain the interval results of voltage amplitude, phase angle and branch power flow of each node. The process of establishing the spatiotemporally correlated multi-noise affine model in step S3 includes: C1: Perform interval predictions for photovoltaic and wind power units respectively, obtain the output prediction intervals of each distributed power source at each time, and calculate the corresponding prediction error sequences respectively; C2: Perform spatial correlation analysis and time shift correlation analysis on the prediction error sequence of distributed power sources in the same region to extract the spatial correlation and dominant time delay relationship between distributed power sources in the region; C3: Construct a covariance matrix based on the prediction error matrix within the region and perform principal component decomposition to extract the dominant shared disturbance mode, obtain the sharing degree of each distributed power source, and determine the regional shared noise figure and node local noise figure according to the interval consistency constraint. C4: Based on the interval prediction results, regional shared noise coefficient and node local noise coefficient, a spatiotemporal correlation multi-noise affine model of node distributed power output is established.

2. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 1, characterized in that, Step S1 includes: A1: Obtain the network topology and line impedance parameters of the distribution network, and construct the network admittance matrix; A2: Based on the given active and reactive power injection information of the nodes, the reference bus settings and the per-unit benchmark, determine the deterministic operating point of the distribution network; A3: Based on the distributed power source prediction interval, prediction error sequence, and load data, uncertainty modeling input parameters are formed. The uncertainty modeling input parameters include the noise set and coefficients corresponding to regional shared disturbances and node local disturbances, interval boundaries, and the upper bound estimation rules and residual noise settings required for nonlinear residual encapsulation.

3. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 2, characterized in that, Step S2 includes: B1: Based on the power flow Jacobian matrix, establish the sensitivity relationship between node voltage and node active and reactive power injection to construct a comprehensive sensitivity index. The specific steps are as follows: B1-1: The power flow linearization of a distribution network at a certain operating point is expressed as: ； in, , These represent the node voltage magnitude and phase angle, respectively. , These represent the active and reactive power injections of the node, respectively. The current Jacobian matrix is ​​the inverse matrix of the current Jacobian matrix. The sensitivity of node voltage to power injection disturbances can be obtained directly; This represents the active power disturbance. This represents reactive power disturbance. This represents the node voltage phase angle increment. This represents the increment of the node voltage amplitude. B1-2: Based on the linearized expression of power flow in the distribution network, considering the deviation caused by the sensitivity in one direction between two nodes, a sensitivity difference index is proposed with the node's own voltage response to its own injection as the benchmark: ； in, Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-active power sensitivity; Represents a node For nodes Voltage-active power sensitivity; Represents a node Its own voltage-reactive power sensitivity; Represents the node Its own voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; Represents a node For nodes Voltage-reactive power sensitivity; For nodes With nodes The difference in active sensitivity between them For nodes With nodes The reactive power sensitivity difference index between them; B1-3: Considering the different contribution ratios of active and reactive power to voltage, construct a comprehensive sensitivity index. : ； Among them, the weighting coefficient Define as a node The ratio of the voltage change generated by active power to the total voltage change generated by power; B2: Construct the expected electrical distance matrix of the distribution network; For the comprehensive sensitivity matrix Normalization and logarithmic transformation are performed: ； in, For nodes With nodes The normalized value of the overall sensitivity compresses all the overall sensitivities to a similar scale. For point With nodes The logarithm of the overall sensitivity is taken after normalization to improve the numerical discrimination. Then the node The coupling relationships of other nodes in the entire network are represented by vectors. The electrical distance between nodes is defined by the Euclidean norm between the coupling feature vectors of two nodes. Considering the fluctuations in distributed power generation output, the distributed power generation output data is grouped into sample vectors according to time periods, and K-means clustering is performed based on Euclidean distance. A typical scenario, among which The probability of occurrence is Calculate the electrical distance matrix in each scenario. The final electrical distance expectation matrix of the distribution network Represented as: ； in, Indicates the typical operating scenario number; This represents the total number of typical scenarios; B3: Attractor propagation clustering is used to determine partition centers and partitioning results; The obtained electrical distance expectation matrix is ​​transformed into a similarity matrix, and then... The responsibility is updated iteratively using AP clustering. and availability : ； ； in, Candidate nodes As a node The suitability of the representative points; For similarity OK Column elements; For similarity OK Column elements; For nodes The suitability of itself as a candidate cluster center; For nodes More suitable as a node compared to other candidate points The degree of representation; Introducing damping coefficient Perform smooth updates to responsibility and availability: ； ； in, The first one is calculated by the original update formula of responsibility. Updated value of the second candidate's responsibility. For the process After the next iteration, the node For candidate representative points Degree of responsibility The first value calculated by the original availability update formula. Secondary candidate availability update value For the process After the next iteration, the node For candidate representative points Availability; For the process After the second iteration, the node For candidate representative points The responsibility level is updated smoothly. For the process After the next iteration, the node For candidate representative points Availability is updated smoothly; For any node ,go through After convergence of the last iteration, choose to make and The node whose sum reaches its maximum value As a node The representative point, if Then node If a node is selected as the cluster center, then nodes with the same representative point are grouped into the same cluster to obtain the final partitioning result.

4. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 3, characterized in that, Step C2 includes: C2-1: Construct a spatial correlation matrix for the uncertainty of distributed power output and quantify the spatial correlation between different units; set up At this moment, node Prediction error of distributed power generation output Represented as: ； in, For nodes The actual output of the distributed power source; This corresponds to the center value of the predicted power; Calculate the Pearson correlation coefficient between any two distributed generation units, and construct the spatial correlation matrix of photovoltaic output uncertainty, as expressed by: ； in, The spatial correlation matrix, for At any given moment The prediction error of distributed power generation output for At any given moment Prediction error of distributed power generation output; C2-2: A time-delay estimation method based on cross-correlation alignment extracts the dominant lag relationship of error fluctuations at different nodes from historical prediction error sequences to quantify time correlation; For any two nodes in the distribution network system , Cross-correlation function Defined as: ； in, In order to be in node at time +S The error sequence, In order to be in At any given moment The error sequence; The time shift step size; when At that time, node Error sequence relative to nodes Lag One time step, otherwise it is ahead; By traversing a finite time offset range The optimal time offset is obtained as follows: ； The cross-correlation is normalized, and a time-form consistency index is defined. for: ； in, and They are nodes , The autocorrelation term.

5. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 4, characterized in that, Step C3 includes: C3-1: Calculate the degree of uncertainty sharing Suppose a certain AP partition Contains The prediction error matrix of a photovoltaic unit within the time window T is expressed as: ； in, , These represent the first distributed power source in , The prediction error at any given time; , These represent the second distributed power source in , The prediction error at any given time; , The first A distributed power source in , The prediction error at any given time; For the first Distributed power output prediction error matrix within each partition; Construct on this basis Covariance matrix of distributed generation prediction error within each partition : ； in, This represents the number of sampling points within the time window. right Eigenvalue decomposition yields: ； in, For the first The eigenvector matrix of each partition represents the shared perturbation direction; For the first The eigenvalue diagonal matrix of each partition represents the importance of each perturbation direction; Define nodes based on the above formulas. Uncertainty sharing index for: ； Among them, eigenvalues satisfy ; The largest eigenvalue of the covariance matrix The corresponding eigenvector of the first 1 element, and , ; for The prediction error covariance matrix within each partition is the first... 1 eigenvalue, Indicates the number of distributed power sources participating in the modeling within the partition; C3-2: Extracting shared noise figure and local noise figure exist At time t, the interval prediction yields the node. Output power range The center value and half width of the interval are specifically represented as follows: ； in, For nodes At any moment The center value of the distributed power generation output prediction interval, For nodes At any moment The half-width of the output prediction interval for distributed power sources For nodes exist The lower bound of the prediction interval is given at any given time. For nodes exist The upper bound of the time prediction interval; Based on the above formula, apply interval consistency constraints to the affine coefficients: ； ； ； in, , These are the affine coefficients corresponding to shared and local uncertainties, respectively.

6. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 5, characterized in that, Step S4 includes: D1: The obtained multi-noise affine output of the distributed power source is uniformly expressed in the form of complex power; For nodes ,exist Complex power expression at time t for: ； in, These are deterministic predicted values; Includes shared noise and local noise; D2: For deterministic linear operations, keep the input noise set unchanged and do not introduce new noise symbols; D3: For reciprocal or division operations, under the condition of non-singularity, a first-order affine approximation based on interval Taylor expansion is used to construct the reciprocal expression, and a higher-order residual noise term is introduced to cover higher-order nonlinear errors. By the definition of affine arithmetic, we can assume: ； in, For deterministic components, For affine perturbation terms, for Consider the affine representation of the state variables under uncertainty at any given time, and satisfy the non-singular condition: ； in, for At this moment The affine coefficients corresponding to each noise element Describing affine variables radius; Then the function In the interval The above is represented as: ； in, The higher-order nonlinear residual noise element generated by Taylor expansion is used to cover higher-order nonlinear errors; The coefficient of the remainder term; D4: For the multiplication of two complex affine variables that share the same noise set, decompose them into linear dominant terms and second-order coupled terms, and encapsulate the second-order coupled terms as bounded residuals in a unified manner. The specific expression is: ； in, , Representing time respectively The first unified spatiotemporal correlated noise set The and the first One affine noise element; For a moment The first uncertain variable containing spatiotemporal correlation noise, For a moment The second uncertainty variable includes spatiotemporal correlation noise. for The deterministic central value, for The deterministic central value, for The The affine coefficients corresponding to each noise element for The Middle Affine coefficients corresponding to each noise element; The linear dominant term is retained as the main source of uncertainty, while the second-order coupled terms are uniformly treated as bounded residuals and covered by a single residual noise, i.e.: ； in, For the reason and The given upper bound estimate, This is a newly added residual noise element.

7. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 6, characterized in that, Step S5 includes: E1: Ignore uncertain disturbance terms and perform power flow calculations only on deterministic power injection to obtain the deterministic operating point voltage; E2: The uncertain node voltage is expressed as the sum of the deterministic component and the disturbance component, and the node current injection relationship is expanded in the vicinity of the deterministic operating point. The voltage disturbance is decomposed into a linear dominant term and a nonlinear residual term. E3: An approximate expression for nodal current injection is constructed based on the first-order expansion result, wherein the denominators of the division operations involved in the expansion process are all deterministic complex numbers; E4: By utilizing the relationship between network current and voltage, current disturbances are mapped to node voltage disturbances to obtain affine expressions for node voltage disturbances, and further, affine expressions for branch power flows are obtained.

8. The distribution network section power flow analysis method based on improved affine arithmetic with spatiotemporal correlation according to claim 7, characterized in that, Step S6 includes: F1: Estimate the upper bound of the nonlinear residual term and introduce an auxiliary residual noise term to over-approximate the nonlinear residual term; F2: Substitute the encapsulated residual terms back into the node voltage perturbation mapping relationship to obtain the final affine expression of the node voltage; F3: Calculate the voltage amplitude range of each node, the voltage phase angle range of each node, and the power flow range of each branch based on the final affine expression.

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