A static power distribution network system observability evaluation method based on a random response surface method

Abstract

The application provides a static power distribution network system observability evaluation method based on a random response surface method. On the basis of using the random response surface method to perform observability analysis on the static power distribution network system, the basis for judging whether the power distribution network system is observable is that: the system is observable only when the observability coefficient matrix has n linearly independent column vectors, and the i th row and the n+i th row cannot be zero vectors at the same time. Further, an index is constructed for performing observability analysis on the static power distribution network system under the scenes of noisy measurement data, missing measurement data and delayed measurement data, so as to ensure the normal and stable operation of the power distribution network system.

Description

Technical Field

[0001] This invention relates to the field of power distribution network system technology, and in particular to a method for evaluating the observability of static power distribution network systems based on the stochastic response surface methodology. Background Technology

[0002] Observability of power systems is a prerequisite for state estimation calculations and has therefore been a key research focus. Observability analysis and quantification of distribution network systems play a crucial role in modern power system research. Observability analysis methods for static distribution network systems include static state estimation, least squares methods, and topology methods. However, the applicability of static state estimation-based methods relies on completely accurate measurement data and is unsuitable for noisy, missing, or delayed data in practical applications. Least squares methods are sensitive to anomalous data and noise, potentially leading to erroneous state estimations. Topology methods are used for large-scale and complex distribution network systems, but have high computational complexity. Quantification indices for the observability of static distribution network systems include observability measurement matrices, information theory indices, and redundancy measures. However, observability measurement matrices lack robustness to data noise; information theory indices perform poorly in high-noise environments and require high data quality, allowing no data loss or delay; redundancy measures require a large number of measurement points, increasing system costs, and excessive redundancy can lead to increased data processing complexity and resource waste.

[0003] Therefore, existing observability analysis methods and observability quantification indicators for static distribution network systems cannot resist noise interference, are unsuitable for scenarios where data loss or delay occurs, and data processing is complex. In actual engineering projects, measurement data contains noise and may be lost or delayed due to sensor malfunctions, etc. Given that existing observability analysis methods and observability quantification indicators for static distribution network systems are completely inadequate to accurately obtain the system's observability in these scenarios, it is necessary to consider noise interference and the problems of measurement data loss and delay in the observability analysis methods and observability quantification indicators for static distribution network systems. Summary of the Invention

[0004] To address the shortcomings and deficiencies of existing technologies, the present invention aims to provide a method for evaluating the observability of static distribution network systems based on the stochastic response surface methodology, and to present a method for judging whether a system is observable. This method considers the randomness of the system and has low computational complexity. Furthermore, it considers scenarios involving the loss and delay of measurement data, and proposes corresponding quantitative indicators for observability. Finally, it integrates observability conditions and observability degree comprehensive indicators to propose a scheme for determining the strength of system observability.

[0005] The present invention specifically adopts the following technical solution:

[0006] This invention first provides a method for determining the observability of a static distribution network system based on the stochastic response surface methodology. Based on the observability analysis of the static distribution network system using the stochastic response surface methodology, the criterion for determining whether the distribution network system is observable is: if and only if the observability coefficient matrix Φ... k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time.

[0007] Furthermore, the method for obtaining the observability coefficient matrix is ​​as follows:

[0008] The stochastic response surface methodology employs a truncated expanded surrogate model:

[0009] The random output y is:

[0010]

[0011] In the formula, φ0, φ1(ξ) i ), φ2(ξ i 2 Let a0, a0, and a0 represent the bases for the zeroth, first, and second order random response surface methods, respectively. i a i,i These represent the corresponding random response surface method coefficients;

[0012] Zero-order random response surface method basis and its corresponding coefficients φ0 and This represents the average of the estimated values ​​of the l-th measurement, as well as the basis for the first- and second-order random response surface methods and their corresponding coefficients. and The coefficients of the random response surface method represent the uncertainty of the estimate of the l-th measurement relative to the i-th state estimate. and This represents the contribution of the i-th state to the uncertainty of the estimate of the l-th measurement;

[0013] set up Let represent the observability coefficient matrix, which is a submatrix of the coefficient matrix with n linearly independent columns; as follows:

[0014]

[0015] Based on this, the observability assessment method for static distribution network systems based on the stochastic response surface methodology of this invention is constructed:

[0016] Based on the above-described method for determining the observability of a static distribution network system, the observability of the distribution network system is quantified by one or more of the following indicators: the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system.

[0017] Among them, the above five indicators can objectively characterize the observability of a distribution network system based on observability. Each indicator targets a different aspect of observability. In specific applications, those skilled in the art can select one or more of them to evaluate the observability strength according to the actual situation. Of course, reducing one or more of them may lead to an imperfect overall evaluation. However, under certain specific conditions (such as significantly weak noise, certain no data loss, or clearly defined low latency scenarios), some evaluations are still effective. Nevertheless, a comprehensive evaluation of the five indicators remains the most complete and preferred solution of this invention. Therefore, this invention provides the following preferred design.

[0018] Furthermore, the specific method for quantifying the observability of a distribution network system is as follows:

[0019] Construct a comprehensive index R to quantify the degree of observability impact total

[0020]

[0021] R1 to R5 are the observability quantification indices corresponding to the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system.

[0022] R total The magnitude of the value reflects the degree of observability of the system; the closer it is to 1, the stronger the observability of the system; the closer it is to 0, the weaker the observability of the system.

[0023] Let R o R represents the rank of the observability coefficient matrix; o When n = n, the system is observable, which is a prerequisite for analyzing the strength of the observability of the system;

[0024] The observability condition R o A comprehensive index R that combines observability quantification to assess the degree of observability impact. total Construct an index R that can quantify the observability of a system. all ;

[0025] R all =R o +R total ,Rall ∈(n,n+1)

[0026] When R all When R ∈ (n, n+0.35), the system is weakly observable; when R ∈ (n, n+0.35), the system is weakly observable. all When R ∈ (n+0.35, n+0.75), the observability of the system is moderate; when R all When n ∈ (n+0.75, n+1), the system is strongly observable;

[0027] If the observability condition R o If n < n, then the system is unobservable.

[0028] Furthermore, the condition number of the matrix is ​​the ratio of the largest singular value to the smallest singular value, that is:

[0029]

[0030] The reciprocal of the condition number is used as the observability quantification index R1:

[0031]

[0032] The closer R1 is to 0, the weakly observable the system is; the closer R1 is to 1, the observable the system is.

[0033] Furthermore, the strength of the observability of the distribution network system is quantified by the contribution of the state to the estimation, specifically as follows:

[0034] According to the surrogate model, the variance of the estimated value of the l-th measurement is:

[0035]

[0036] The contribution rate is defined as the ratio of the contribution of the i-th state to the variance of the estimated value of the l-th measurement.

[0037]

[0038] in,

[0039] The observability quantification index R² is constructed as follows:

[0040]

[0041] If the system is strongly observable, R² is close to 1; if the system is weakly observable, R² is close to 0.

[0042] Furthermore, the observability of the distribution network system is quantified by observing the impact of noise on the observability of the system, specifically as follows:

[0043] The ratio of the noise variance of the l-th measurement to the variance of the estimated value is defined as the interference rate:

[0044]

[0045] The observability quantification index R3 is constructed as follows:

[0046]

[0047] in, This indicates the average interference rate of the measurement;

[0048] If the system is weakly observable, R3 is close to 0.

[0049] Furthermore, the impact of lost observation data on the observability of the distribution network system is used to quantify the strength of observability.

[0050] This represents the variance of the estimated value of the l-th measurement assuming no data loss. The variance of the estimated value of the l-th measurement after data loss; This represents the variance of the estimated value of the l-th measurement due to the loss of observation data;

[0051] The data loss impact factor is defined as the ratio of the difference in variance before and after the occurrence of data loss in the l-th measurement to the variance of the estimated value when data loss did not occur.

[0052]

[0053] The observability quantification index R4 is constructed as follows:

[0054]

[0055] in, This indicates the average data loss impact factor in the measurement;

[0056] If the system is weakly observable, R4 is close to 0.

[0057] Furthermore, the strength of the observability of the distribution network system is quantified by the impact of observation data delay on system observability, specifically as follows:

[0058] The variance of the estimated value of the l-th measurement without data delay. The variance of the estimated value of the l-th measurement after the data delay occurs; This represents the variance of the estimated value of the l-th measurement due to the delay in the observation data;

[0059] The ratio of the difference in variance of the observed data before and after the data delay in the l-th measurement to the variance of the estimated value without the data delay is defined as the data delay impact factor.

[0060]

[0061] The observability quantification index R5 is constructed as follows:

[0062]

[0063] in, This indicates the average data delay impact factor of the measurement;

[0064] If the system is weakly observable, then R5 is close to 0.

[0065] The present invention also claims protection for a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it adopts a static distribution network system observability assessment method based on the stochastic response surface method as described above, which at least includes the above observability judgment module, and preferably includes a quantitative assessment module.

[0066] Furthermore, a static distribution network system observability assessment device based on the stochastic response surface methodology includes an observability judgment module. This module determines whether the distribution network system is observable based on an observability analysis performed using the stochastic response surface methodology. The basis for this determination is: the observability coefficient matrix Φ... k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time.

[0067] Furthermore, it also includes a quantitative evaluation module: based on the observation judgment module's determination that the static distribution network system has observability, it quantifies the strength of the observability of the distribution network system through one or more of the following indicators: the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the system observability, the impact of observation data loss on the system observability, and the impact of observation data delay on the system observability.

[0068] Furthermore, the quantitative evaluation module employs a comprehensive index R to quantify the degree of observability impact. total

[0069]

[0070] R1 to R5 are the observability quantification indices corresponding to the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system.

[0071] R totalThe magnitude of the value reflects the degree of observability of the system; the closer it is to 1, the stronger the observability of the system; the closer it is to 0, the weaker the observability of the system.

[0072] Let R o R represents the rank of the observability coefficient matrix; o When n = n, the system is observable, which is a prerequisite for analyzing the strength of the observability of the system;

[0073] The observability condition R o A comprehensive index R that combines observability quantification to assess the degree of observability impact. total Construct an index R that can quantify the observability of a system. all ;

[0074] R all =R o +R total ,R all ∈(n,n+1)

[0075] When R all When R ∈ (n, n+0.35), the system is weakly observable; when R ∈ (n, n+0.35), the system is weakly observable. all When R ∈ (n+0.35, n+0.75), the observability of the system is moderate; when R all When n ∈ (n+0.75, n+1), the system is strongly observable;

[0076] If the observability condition R o If n < n, then the system is unobservable.

[0077] Furthermore, the condition number of the matrix is ​​the ratio of the largest singular value to the smallest singular value, that is:

[0078]

[0079] The reciprocal of the condition number is used as the observability quantification index R1:

[0080]

[0081] The closer R1 is to 0, the weakly observable the system is; the closer R1 is to 1, the observable the system is.

[0082] Furthermore, the strength of the observability of the distribution network system is quantified by the contribution of the state to the estimation, specifically as follows:

[0083] According to the surrogate model, the variance of the estimated value of the l-th measurement is:

[0084]

[0085] The contribution rate is defined as the ratio of the contribution of the i-th state to the variance of the estimated value of the l-th measurement.

[0086]

[0087] in,

[0088] The observability quantification index R² is constructed as follows:

[0089]

[0090] If the system is strongly observable, R² is close to 1; if the system is weakly observable, R² is close to 0.

[0091] Furthermore, the observability of the distribution network system is quantified by observing the impact of noise on the observability of the system, specifically as follows:

[0092] The ratio of the noise variance of the l-th measurement to the variance of the estimated value is defined as the interference rate:

[0093]

[0094] The observability quantification index R3 is constructed as follows:

[0095]

[0096] in, This indicates the average interference rate of the measurement;

[0097] If the system is weakly observable, R3 is close to 0.

[0098] Furthermore, the impact of lost observation data on the observability of the distribution network system is used to quantify the strength of observability.

[0099] This represents the variance of the estimated value of the l-th measurement assuming no data loss. The variance of the estimated value of the l-th measurement after data loss; This represents the variance of the estimated value of the l-th measurement due to the loss of observation data;

[0100] The data loss impact factor is defined as the ratio of the difference in variance before and after the occurrence of data loss in the l-th measurement to the variance of the estimated value when data loss did not occur.

[0101]

[0102] The observability quantification index R4 is constructed as follows:

[0103]

[0104] in, This indicates the average data loss impact factor in the measurement;

[0105] If the system is weakly observable, R4 is close to 0.

[0106] Furthermore, the strength of the observability of the distribution network system is quantified by the impact of observation data delay on system observability, specifically as follows:

[0107] The variance of the estimated value of the l-th measurement without data delay. The variance of the estimated value of the l-th measurement after the data delay occurs; This represents the variance of the estimated value of the l-th measurement due to the delay in the observation data;

[0108] The ratio of the difference in variance of the observed data before and after the data delay in the l-th measurement to the variance of the estimated value without the data delay is defined as the data delay impact factor.

[0109]

[0110] The observability quantification index R5 is constructed as follows:

[0111]

[0112] in, This indicates the average data delay impact factor of the measurement;

[0113] If the system is weakly observable, then R5 is close to 0.

[0114] Compared to existing technologies, this invention and its preferred embodiments first propose an observability analysis method based on the stochastic response surface methodology, and provide a method for determining whether a distribution network system is observable: the system is observable if and only if the observability coefficient matrix has n linearly independent column vectors. Furthermore, it proposes a quantitative index for observability based on the stochastic response surface methodology to achieve a quantitative assessment of the observability strength of the system. Attached Figure Description

[0115] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0116] Figure 1 This is a schematic diagram of the observability evaluation process according to an embodiment of the present invention. Detailed Implementation

[0117] In the following, specific embodiments of this application will be described in detail with reference to the accompanying drawings. Based on these detailed descriptions, those skilled in the art will be able to clearly understand and implement this application. Without departing from the principles of this application, features from various embodiments can be combined to obtain new implementations, or certain features from some embodiments can be substituted to obtain other preferred implementations.

[0118] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below, along with accompanying drawings, for detailed explanation:

[0119] 1. The principle of the random response surface methodology

[0120] (1) Mapping transformation of random input

[0121] The i-th state random variable x is distributed according to the following standard probability distribution. i Mapping to a new random variable ξ i :

[0122] x i =F i -1 (T i (ξ i ),i=1,2,...,n, (1)

[0123] Where F i -1 (.) represents x i The inverse cumulative distribution function, T i Indicates ξ i The cumulative distribution function.

[0124] (2) Approximation of the system output function

[0125] In the random response surface method, the random output y can be approximated as:

[0126]

[0127] In the formula, y is the system output, and ξ = [ξ1, ξ2, ..., ξ]. n [ ] is a vector of random variables that follow a standard probability distribution, and its corresponding random response surface method basis is φ. i (ξ), a i It is the coefficient of the i-th random response surface method.

[0128] n p = (n+p)! / (n!p!)-1, and p is the maximum order of the basis functions of the random response surface method.

[0129] Based on the coefficients of the random response surface methodology, the mean and variance of the output can be directly obtained, as shown below:

[0130]

[0131] (3) Proxy Model

[0132] To model the response surface with low computational complexity while maintaining high accuracy, this embodiment employs truncation expansion, as follows:

[0133]

[0134] In the formula, φ0, φ1(ξ) i ), φ2(ξ i 2 Let a0 represent the bases for the zeroth, first, and second order random response surface methods, respectively.

[0135] a i a i,i This represents the corresponding random response surface method coefficient.

[0136] 2. Observability Analysis Method Based on Stochastic Response Surface Methodology

[0137] To implement the surrogate model, some placement points are selected by combining a finite number of samples of ξ. Considering N combinations of placement points, a polynomial chaotic basis can be directly obtained, and the system output can be calculated through the system model. Formally, the surrogate model has

[0138] Y k =HA k (5)

[0139]

[0140]

[0141] in, It is a measurement matrix composed of the measurement values ​​of N samples; The basis matrix is ​​composed of random response surface method bases; ξ s,i It is the i-th element of the s-th sample; It is a coefficient matrix; Represents the random response surface method coefficients for the i-th state and the l-th measurement.

[0142] Suppose a random variable ξ i It follows a Gaussian distribution. In this case, the corresponding Hermitian polynomial is φ0=1, φ1(ξ s,i )=ξ s,i and Therefore, the elements of the locus of points are determined by the union of the zero-sum roots of a higher-order one-dimensional Hermitian polynomial. Then, the coefficient matrix A can be obtained through the basis matrix and the measurement matrix. k ,

[0143] A k =H -1 Y k (8)

[0144] Based on the stochastic response surface methodology, this invention proposes an observability condition to test whether a system is observable. Due to the orthogonality property, the average value of the first-order and second-order stochastic response surface methodology bases is zero; therefore, the zero-order stochastic response surface methodology base and its corresponding coefficients φ0 and... This represents the average of the estimated values ​​of the l-th measurement, as well as the basis for the first- and second-order random response surface methods and their corresponding coefficients. and The coefficients of the random response surface method represent the uncertainty of the estimate of the l-th measurement relative to the i-th state estimate. and This represents the contribution of the i-th state to the uncertainty of the estimate of the l-th measurement.

[0145] If the contribution of the i-th state to the uncertainty of the estimate at the l-th measurement is zero, then the latter remains unchanged relative to that state; that is, the i-th state cannot be inferred from the l-th measurement. To uniquely infer n states from a given set of measurements, n valid measurements are needed, for which the contributions of the state to the uncertainty of the estimates of these measurements are linearly independent. Let... The observability coefficient matrix is ​​a submatrix of the coefficient matrix with n linearly independent columns. As follows:

[0146]

[0147] A method for determining whether a distribution network system is observable: The observable coefficient matrix Φ is observable if and only if... k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time.

[0148] 3. Observability Quantification Indicators Based on Stochastic Response Surface Methodology

[0149] In static distribution network systems, observability analysis is a crucial step in ensuring accurate estimation of system state using limited measurement data. However, in practical applications, noise, loss, and delay in measurement data significantly impact system observability. These issues not only affect the accuracy and reliability of system state estimation but also have a profound impact on the operation, monitoring, and management of the distribution network.

[0150] Noise is an unavoidable error in measurement data, mainly originating from inherent errors of measuring equipment, environmental interference, and losses and interference during signal transmission. Noise reduces the accuracy of measurement data, leading to increased errors in system state estimation and inaccurate state estimation results, thus affecting the accuracy of observability analysis. Noise introduces additional uncertainty; excessive uncertainty reduces system observability, making it difficult to accurately determine the actual operating state of the system. Noise affects the effectiveness of fusion and filtering, resulting in significant errors in the fused data. Noise interferes with the calculation of observability quantification indicators and affects the calculation of the rank of the observability metric matrix, leading to inaccurate observability analysis results.

[0151] Data loss refers to the loss of some measurement data during data transmission due to various reasons. Data loss leads to incomplete data sources for system state estimation, resulting in inaccurate system state estimates and affecting the results of observability analysis. Data loss also reduces system reliability, especially at critical nodes, where data loss can have a significant impact on the operation of the entire distribution network. Furthermore, data loss can lead to inaccurate calculations of observability quantification indicators, affecting the overall system assessment.

[0152] Latency refers to the time delay required for measurement data to go from acquisition to processing and analysis. Latency affects the real-time monitoring and response speed of the system, making it difficult to estimate and control the system state in real time, thus reducing the system's observability. Latency interferes with the multi-sensor data fusion and filtering process, causing the fused data to fail to accurately reflect the actual state of the system, affecting the results of observability analysis. Latency also affects the real-time calculation of observability quantification indicators, making these indicators unable to accurately reflect the current system state, thereby affecting system evaluation and decision-making.

[0153] In summary, the embodiments of the present invention further construct an index that can still perform observability analysis on a static distribution network system even in scenarios where the measurement data contains noise, the measurement data is missing, and the measurement data is delayed, so as to ensure the normal and stable operation of the distribution network system.

[0154] Existing observability assessments of power distribution systems generally only consider whether the system is observable, without quantifying the degree of observability. Therefore, this invention proposes indicators to quantify the degree of observability based on observability conditions, i.e., to quantify the strength of observability of the power distribution network system. The following five quantitative indicators are proposed:

[0155] (1) Condition number

[0156] To ensure the numerical stability of the estimated state, the singular values ​​of the observability coefficient matrix cannot differ too much, i.e., the condition number cannot be too large; otherwise, the observability coefficient matrix may be ill-conditioned. If the observability coefficient matrix is ​​ill-conditioned, observability analysis of the system cannot be performed using the observability coefficient matrix, meaning the system is unobservable. The condition number of the matrix is ​​the ratio of its largest singular value to its smallest singular value, i.e.

[0157]

[0158] The first observability quantification metric, R1, is the reciprocal of the condition number, i.e.

[0159]

[0160] Definition 1: If the condition number is very large or becomes infinite, i.e., the smaller R1 is, the closer it is to 0, then the system is weakly observable. If the condition number is close to 1, i.e., the larger R1 is, the closer it is to 1, then the system is observable.

[0161] (2) Contribution of state to estimation

[0162] According to the surrogate model, the variance of the estimated value of the l-th measurement is obtained through...

[0163]

[0164] The contribution rate is defined as the ratio of the contribution of the i-th state to the variance of the estimated value of the l-th measurement.

[0165]

[0166] It follows The contribution rate represents the influence of the state on the estimated value of the measurement. A larger contribution rate means that the state has a greater influence on the estimated value of the measurement, and vice versa.

[0167] Definition 2: If all contribution rates If the value of the i-th state is less than a small positive value (e.g., 0.1%), that state is weakly observable. Otherwise, it is strongly observable. If all states are strongly observable, then the system is strongly observable. Otherwise, the system is weakly observable.

[0168] The second observability quantification metric, R², is:

[0169]

[0170] If the system is strongly observable, then the contribution rates of all states are relatively large, close to 1, and the average index R2 is also large, close to 1. If the system is weakly observable, then not all states have contribution rates close to 1, and the average index R2 is not large, close to 0. Therefore, the magnitude of index R2 can reflect the observability of the system.

[0171] (3) The impact of observation noise on system observability

[0172] if The contribution of the given i-th state to the variance of the estimate of the l-th measurement is close to or less than the variance of the measurement noise. Therefore, its impact is difficult to distinguish from the impact of noise variance.

[0173] The ratio of the noise variance of the l-th measurement to the variance of the estimated value is defined as the interference rate.

[0174]

[0175] Definition 3: For a noisy measurement environment, when all contribution rates Less than the corresponding interference rate (V) (1) V (2) ,...,V (m) When ), the i-th state is weakly observable.

[0176] The third observability quantification indicator, R3, is,

[0177]

[0178] In equation (16) This indicates the average interference rate of the measurement.

[0179] If the system is weakly observable, the interference rate is closer to 1 than the contribution rate, and the average interference rate is also close to 1. In this case, R3 is small, close to 0. Conversely, R3 is large. In this case, the third indicator R3 can also reflect the observability of the system through its value.

[0180] (4) The impact of lost observation data on system observability

[0181] This represents the variance of the estimated value of the l-th measurement assuming no data loss. This represents the variance of the estimated value of the l-th measurement after data loss. This represents the variance of the estimated value of the l-th measurement due to the loss of observation data.

[0182] The data loss impact factor is defined as the ratio of the difference in variance before and after the occurrence of data loss in the l-th measurement to the variance of the estimated value when no data loss occurred.

[0183]

[0184] Definition 4: For measurement scenarios with data loss, when all contribution rates Less than the corresponding data loss impact factor (P) (1) ,P (2) ,...,P (m) When ), the i-th state is weakly observable.

[0185] The fourth observability quantification indicator, R4, is...

[0186]

[0187] In equation (18) This indicates the average data loss impact factor in the measurement.

[0188] If the system is weakly observable, the data loss impact factor is closer to 1 than the contribution rate, and the average data loss impact factor is also close to 1. In this case, R4 is small, close to 0. Conversely, R4 is large. In this case, the fourth indicator R4 can also reflect the observability of the system through its value.

[0189] (5) The impact of observation data delay on system observability

[0190] The variance of the estimated value of the l-th measurement without data delay. This represents the variance of the estimated value of the l-th measurement after the data delay. This represents the variance of the estimated value of the l-th measurement due to the delay in the observation data.

[0191] The ratio of the difference in variance of the observed data before and after the data delay in the l-th measurement to the variance of the estimated value without the data delay is defined as the data delay impact factor.

[0192]

[0193] Definition 5: For measurement scenarios with data latency, when all contribution rates Less than the corresponding data delay impact factor (T) (1) ,T (2) ,...,T (m) When ), the i-th state is weakly observable.

[0194] The fifth observability quantification indicator, R5, is...

[0195]

[0196] In equation (20) This represents the average data delay impact factor of the measurement.

[0197] If the system is weakly observable, the data delay impact factor is closer to 1 than the contribution rate, and the average data delay impact factor is also close to 1. In this case, R5 is small, close to 0. Conversely, R5 is large. In this case, the fifth indicator R5 can also reflect the observability of the system through its value.

[0198] Based on the above five indicators, a comprehensive indicator R is proposed to quantify the degree of observability impact. total ,

[0199]

[0200] R total The magnitude of the value reflects the degree of observability of the system; the closer it is to 1, the stronger the observability of the system; the closer it is to 0, the weaker the observability of the system.

[0201] 4. Comprehensive Observability Analysis and Quantitative Indicators of Systems Based on Stochastic Response Surface Methodology

[0202] Let R o Let represent the rank of the observability coefficient matrix. From the observability analysis method based on the stochastic response surface approach, it is known that ... k When the system has n linearly independent column vectors, it is observable, i.e., Robservable. o When n = n, the system is observable. System observability is a prerequisite for analyzing the strength of system observability.

[0203] The observability condition R o A comprehensive index R that combines observability quantification to assess the degree of observability impact. total A general, quantifiable index R for the observability of a system is proposed. all .

[0204] R all =R o +R total ,R all ∈(n,n+1) (22)

[0205] Based on the magnitude of the random disturbance rate, the overall observability index R of the quantifiable system can be determined. all It is divided into the following three levels, representing the strength of observability.

[0206] When R all When R ∈ (n, n+0.35), the system is weakly observable; when R ∈ (n, n+0.35), the system is weakly observable. all When R ∈ (n+0.35, n+0.75), the observability of the system is moderate; when R all When ∈(n+0.75,n+1), the system is strongly observable; according to R allThe size can be divided into three levels of observability intensity: strong, medium, and weak.

[0207] If the observability condition R o If n < n, then the system is unobservable. In this case, there is no need to further discuss the strength of the system's observability. The above process is as follows: Figure 1 As shown.

[0208] Based on the above design, this invention also provides an observability assessment device for a static distribution network system based on the stochastic response surface methodology, including an observability judgment module. This module determines whether the distribution network system is observable based on the observability analysis performed using the stochastic response surface methodology. The criterion is: if and only if the observability coefficient matrix Φ... k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time.

[0209] Furthermore, it also includes a quantitative evaluation module: based on the observationability judgment module's determination that the static distribution network system has observability, it quantifies the strength of the observability of the distribution network system through one or more of the following indicators: the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the system observability, the impact of observation data loss on the system observability, and the impact of observation data delay on the system observability. The selection of one, multiple, or even all of these indicators can be referred to the description in the above method section by those skilled in the art.

[0210] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0211] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0212] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0213] The foregoing has shown and described the basic principles, main features, and advantages of this disclosure. Those skilled in the art should understand that this disclosure is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this disclosure. Various changes and modifications can be made to this disclosure without departing from its spirit and scope, and all such changes and modifications fall within the scope of this disclosure as claimed.

[0214] This patent is not limited to the above-described preferred embodiment. Anyone can derive other forms of observability assessment method for static distribution network systems based on the stochastic response surface methodology under the guidance of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.

Claims

1. A method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology, characterized in that: Based on the observability analysis of a static distribution network system using the stochastic response surface methodology, the criterion for determining whether a distribution network system is observable is: if and only if the observability coefficient matrix Φ k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time. The method for obtaining the observability coefficient matrix is ​​as follows: The stochastic response surface methodology employs a truncated expanded surrogate model: The random output y is: In the formula, φ0, φ1(ξ) i ), Let a0, a0, and a0 represent the bases for the zeroth, first, and second order random response surface methods, respectively. i a i,i These represent the corresponding random response surface method coefficients; Zero-order random response surface method basis and its corresponding coefficients φ0 and This represents the average value of the estimated value of the l-th measurement, and the basis of the first- and second-order random response surface methods and their corresponding coefficients (φ1(ξ)). s,i ), )and The coefficients of the random response surface method represent the uncertainty of the estimate of the l-th measurement relative to the i-th state estimate. and This represents the contribution of the i-th state to the uncertainty of the estimate of the l-th measurement; set up Let represent the observability coefficient matrix, which is a submatrix of the coefficient matrix with n linearly independent columns; as follows:

2. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 1, characterized in that: Based on the determination that the static distribution network system has observability, the observability of the distribution network system is quantified by one or more of the following indicators: the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system.

3. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 2, characterized in that: The specific methods for quantifying the observability of a distribution network system are as follows: Construct a comprehensive index R to quantify the degree of observability impact total R1 to R5 are the observability quantification indices corresponding to the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system. R total The magnitude of the value reflects the degree of observability of the system; the closer it is to 1, the stronger the observability of the system; the closer it is to 0, the weaker the observability of the system. Let R o R represents the rank of the observability coefficient matrix; o When n = n, the system is observable, which is a prerequisite for analyzing the strength of the observability of the system; The observability condition R o A comprehensive index R that combines observability quantification to assess the degree of observability impact. total Construct an index R that can quantify the observability of a system. all ; R all =R o +R total ,R all ∈(n,n+1) When R all When R ∈ (n, n+0.35), the system is weakly observable; when R ∈ (n, n+0.35), the system is weakly observable. all When R ∈ (n+0.35, n+0.75), the observability of the system is moderate; when R all When n ∈ (n+0.75, n+1), the system is strongly observable; If the observability condition R o If n < n, then the system is unobservable.

4. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 2 or 3, characterized in that: The strength of observability of a distribution network system can be quantified using the observability coefficient matrix as follows: The condition number of the matrix is ​​the ratio of the largest singular value to the smallest singular value, that is: The reciprocal of the condition number is used as the observability quantification index R1: The closer R1 is to 0, the weakly observable the system is; the closer R1 is to 1, the observable the system is.

5. The observability assessment method for a static distribution network system based on the stochastic response surface methodology according to claim 2 or 3, characterized in that: The strength of observability of a distribution network system is quantified by the contribution of state to the estimation. According to the surrogate model, the variance of the estimated value of the l-th measurement is: The contribution rate is defined as the ratio of the contribution of the i-th state to the variance of the estimated value of the l-th measurement. in, The observability quantification index R² is constructed as follows: If the system is strongly observable, R² is close to 1; if the system is weakly observable, R² is close to 0.

6. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 2 or 3, characterized in that: Quantifying the observability of a distribution network system by observing the impact of noise on system observability specifically involves: The ratio of the noise variance of the l-th measurement to the variance of the estimated value is defined as the interference rate: The observability quantification index R3 is constructed as follows: in, This indicates the average interference rate of the measurement; If the system is weakly observable, R3 is close to 0.

7. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 2 or 3, characterized in that: Quantifying the observability of a distribution network system by assessing the impact of lost observation data on system observability specifically involves: This represents the variance of the estimated value of the l-th measurement assuming no data loss. The variance of the estimated value of the l-th measurement after data loss occurs; This represents the variance of the estimated value of the l-th measurement due to the loss of observation data; The data loss impact factor is defined as the ratio of the difference in variance before and after the occurrence of data loss in the l-th measurement to the variance of the estimated value when data loss did not occur. The observability quantification index R4 is constructed as follows: in, This indicates the average data loss impact factor in the measurement; If the system is weakly observable, R4 is close to 0.

8. The method for evaluating the observability of a static distribution network system based on the stochastic response surface methodology according to claim 2 or 3, characterized in that: Quantifying the observability of a distribution network system by analyzing the impact of observation data delay on system observability specifically involves: The variance of the estimated value of the l-th measurement without data delay. The variance of the estimated value of the l-th measurement after the data delay occurs; This represents the variance of the estimated value of the l-th measurement due to the delay in the observation data; The ratio of the difference in variance of the observed data before and after the data delay in the l-th measurement to the variance of the estimated value without the data delay is defined as the data delay impact factor. The observability quantification index R5 is constructed as follows: in, This indicates the average data delay impact factor of the measurement; If the system is weakly observable, then R5 is close to 0.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, it employs the method as described in any one of claims 1-8.

10. A static distribution network system observability assessment device based on the stochastic response surface methodology, characterized in that: This includes an observability assessment module, which, based on observability analysis of the static distribution network system using the stochastic response surface methodology, determines whether the distribution network system is observable. The basis for this determination is: the observability coefficient matrix Φ... k The system is observable when it has n linearly independent column vectors, and the i-th row and the (n+i)-th row cannot both be zero vectors at the same time. The method for obtaining the observability coefficient matrix is ​​as follows: The stochastic response surface methodology employs a truncated expanded surrogate model: The random output y is: In the formula, φ0, φ1(ξ) i ), φ2(ξ i 2 Let a0, a0, and a0 represent the bases for the zeroth, first, and second order random response surface methods, respectively. i a i,i These represent the corresponding random response surface method coefficients; Zero-order random response surface method basis and its corresponding coefficients φ0 and This represents the average value of the estimated value of the l-th measurement, and the basis of the first- and second-order random response surface methods and their corresponding coefficients (φ1(ξ)). s,i ), )and The coefficients of the random response surface method represent the uncertainty of the estimate of the l-th measurement relative to the i-th state estimate. and This represents the contribution of the i-th state to the uncertainty of the estimate of the l-th measurement; set up Let represent the observability coefficient matrix, which is a submatrix of the coefficient matrix with n linearly independent columns; as follows:

11. The observability assessment device for static distribution network systems based on the stochastic response surface methodology according to claim 10, characterized in that: It also includes a quantitative evaluation module: based on the observability of the static distribution network system determined by the observability judgment module, it quantifies the observability of the distribution network system by one or more of the following indicators: the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of observation data loss on the observability of the system, and the impact of observation data delay on the observability of the system.

12. The static distribution network system observability assessment device based on the stochastic response surface methodology according to claim 11, characterized in that: The quantitative evaluation module uses a comprehensive index R to quantify the degree of observability impact. total R1 to R5 are the observability quantification indices corresponding to the condition number of the observability coefficient matrix, the contribution of the state to the estimation, the impact of observation noise on the observability of the system, the impact of lost observation data on the observability of the system, and the impact of observation data delay on the observability of the system. R total The magnitude of the value reflects the degree of observability of the system; the closer it is to 1, the stronger the observability of the system; the closer it is to 0, the weaker the observability of the system. Let R o R represents the rank of the observability coefficient matrix; o When n = n, the system is observable, which is a prerequisite for analyzing the strength of the observability of the system; The observability condition R o A comprehensive index R that combines observability quantification to assess the degree of observability impact. total Construct an index R that can quantify the observability of a system. all ; R all =R o +R total ,R all ∈(n,n+1) When R all When R ∈ (n, n+0.35), the system is weakly observable; when R ∈ (n, n+0.35), the system is weakly observable. all When R ∈ (n+0.35, n+0.75), the observability of the system is moderate; when R all When n ∈ (n+0.75, n+1), the system is strongly observable; If the observability condition R o If n < n, then the system is unobservable.

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