A method and system for distribution network risk assessment based on a Dirichlet process hybrid model and semi-invariant method

Abstract

This invention proposes a distribution network risk assessment method and system based on a Dirichlet process hybrid model and a semi-invariant method. The method includes: introducing a Dirichlet process hybrid model to perform Bayesian nonparametric clustering on distributed generation output samples, and using adaptive kernel density estimation to fit probability density within each cluster to obtain a probability distribution model of distributed generation output; constructing a probabilistic power flow solution method combining semi-invariants and series expansion to address the random fluctuation characteristics of distributed generation and load in the distribution network, thereby describing the probability distribution of node state variables and branch power flows, and providing basic probabilistic power flow data support for subsequent risk assessment; and constructing distribution network risk assessment indicators based on distribution entropy theory to characterize the risk of exceeding limits for state variables, including voltage and power flow, and further obtaining the risk caused by the uncertainty of the probability distribution of state variables, thus achieving distribution network risk assessment.

Description

Technical Field

[0001] This invention proposes a distribution network risk assessment method and system based on a Dirichlet process hybrid model and a semi-invariant method, which relates to the field of power system distribution network analysis. Background Technology

[0002] With the widespread integration of distributed generation, the operation mode of the power system is undergoing profound changes. The complementarity and coordination between distributed generation and the traditional large-scale power grid supply mode make it an effective way to comprehensively utilize existing resources and equipment to provide users with highly reliable and high-quality electricity. However, this transformation has also significantly impacted the operating status of the distribution network. On the one hand, the integration of distributed generation alters the power flow characteristics of the traditional distribution network, thereby affecting the load distribution and current flow direction. On the other hand, renewable energy sources such as distributed generation depend on changes in the external environment, and their power generation output exhibits strong volatility and uncertainty, potentially leading to problems such as reverse overload and local voltage runaway in the distribution network, further threatening the safety and stable operation of the power grid. Against this backdrop, risk assessment, as a process of quantitatively analyzing the probability and consequences of uncertain events in the system, is particularly crucial in the operational analysis of distribution networks that include distributed generation. However, traditional power flow calculation methods based on deterministic assumptions are insufficient to accurately characterize the impact of complex uncertainties on the actual operating status of the distribution network, and also struggle to effectively predict potential operational risks.

[0003] Existing probabilistic power flow analysis and risk assessment of distribution networks typically employ simulation, approximation, and analytical methods. However, due to the overlapping uncertainties of source and load after the integration of distributed renewable energy, and the high dimensionality and computational demands of the assessment scenarios, existing methods still have significant limitations in terms of efficiency, accuracy, and the completeness of risk characterization. Consequently, the assessment results cannot comprehensively and reliably support engineering scheduling and risk management. Summary of the Invention

[0004] In view of this, in order to fill the gaps and deficiencies in the existing technology, this invention proposes a distribution network risk assessment method and system based on the Dirichlet process hybrid model and the semi-invariant method, which is used to effectively quantify the operation risk of the distribution network.

[0005] This invention proposes a distribution network risk assessment method and system based on a Dirichlet process hybrid model and a semi-invariant method, comprising the following:

[0006] According to a first aspect of the present invention, the present invention proposes a distribution network risk assessment method based on a Dirichlet process hybrid model and a semi-invariant method, characterized in that it includes the following:

[0007] A Dirichlet process mixture model is introduced to perform Bayesian nonparametric clustering on the output samples of distributed generation, and an adaptive kernel density estimation is used to fit the probability density within each cluster to obtain the probability distribution model of distributed generation output.

[0008] To address the random fluctuation characteristics of distributed generation and load in distribution networks, a probabilistic power flow solution method combining semi-invariants and series expansion is constructed to describe the probability distribution of node state variables and branch power flow, while providing basic probabilistic power flow data support for subsequent risk assessment.

[0009] Based on the theory of distributed entropy, a risk assessment index for distribution networks is constructed to characterize the risk of exceeding limits of state variables, including voltage and power flow, and further to obtain the risk caused by the uncertainty of the probability distribution of state variables, thereby realizing the risk assessment of distribution networks.

[0010] Furthermore, the aforementioned method for assessing distribution network risk based on a Dirichlet process hybrid model and a semi-invariant method also includes the following steps:

[0011] Step S1: Establish a Dirichlet process hybrid model to adaptively identify the data cluster structure and extract uncertain information without pre-setting the number of categories, thereby realizing cluster analysis and probability density estimation of distributed power sources.

[0012] Step S2: Establish an adaptive nonparametric kernel density estimation model, including obtaining the probability distribution of kernel density estimation based on the distribution characteristics of distributed power generation output data;

[0013] Step S3: Use semi-invariants and series expansion to perform probabilistic power flow calculations on distribution networks containing distributed generation sources, and quantify the degree of exceeding limits of branch power flow and node voltage probability distribution based on distribution entropy, thereby realizing the risk assessment of distribution network operation.

[0014] Step S4: Conduct a risk assessment of the distribution network including distributed generation, including comprehensively considering the losses caused by node voltage exceeding limits and line power flow exceeding limits, and quantitatively calculate the distribution network exceeding limit risk index accordingly; construct an index based on distribution entropy theory to measure the degree of change in the probability distribution including node voltage and line power flow after random factors are connected to the distribution network, so as to assess the operational risks caused by distribution changes.

[0015] Further, step S1 includes the following:

[0016] Step S11: Assume the observed data comes from a mixed distribution of several unknown categories. ;

[0017] Selecting distributed power generation output data As data to be clustered;

[0018] Suppose the data to be clustered follows a set of parameters The distribution of data is given by n, where n is the number of data points. Data belonging to the same parameter φ are classified into the same category. The distributed power output data x to be clustered is divided into k categories, where k < n, indicating that the number of categories k is less than the total number of data points n.

[0019] Step S12: Let G be a random probability distribution on a measure space.

[0020] The measure space is arbitrarily partitioned as: a = {a1, a2, …, a r},

[0021] Furthermore, set Following a Dirichlet distribution, we obtain the following:

[0022] ;(1);

[0023] Where α0 is a hyperparameter, and α0>0, used to represent the degree of dispersion of G; G0 is the baseline distribution;

[0024] Step S13: For a Dirichlet process, if the observed values ​​are sampled from the random measure G... Then its posterior distribution satisfies the following:

[0025] (2);

[0026] Where P is the probability of occurrence; For observations Quantity; for The Dirac function; N is the total number of observations.

[0027] Furthermore, step S1 also includes the following:

[0028] Step S14: Construct the random probability distribution G using the Chinese restaurant process, including:

[0029] Consider the restaurant as having an infinite number of tables; let x be the i-th customer entering the restaurant. i The tables in the restaurant for customers to sit at are Representation; baseline distribution G0 and parameters Let x and y represent the parameters of the k-th table; x and y represent the parameters of the x-th table. i A customer enters the restaurant and records the table. The number of customers already seated is m k The i-th customer is proportional to m k The probability of sitting at the table Above, also proportional to The probability of a customer sitting at a new table is represented as:

[0030] (3);

[0031] Step S15: Extend the Dirichlet process into a Dirichlet process hybrid model, resulting in:

[0032] (4);

[0033] Clustering distributed power source output data using a Dirichlet process hybrid model constructed from the Chinese restaurant process yields the following results:

[0034] (5);

[0035] in, It follows a Gaussian distribution; The mean and variance are given.

[0036] Step S16: For an existing cluster k, given the parameters of cluster k, sample x i Conditional probabilities include:

[0037] (6);

[0038] in, and The posterior mean and variance of cluster k are obtained by updating the data based on the observation data; Let k be the updated number of samples in cluster k.

[0039] The expression for the conditional probability of the new cluster k+1 is:

[0040] (7);

[0041] in, and Let be the prior mean and variance of the new cluster; Count the prior samples for the new cluster;

[0042] Step S17: After calculating the conditional probability, the Gibbs sampling algorithm is used to update the class assignment for each sample. Through multiple iterations, the optimal class assignment result is finally converged.

[0043] Further, step S2 includes the following:

[0044] Step S21: Based on the distributed power output data's distribution characteristics, including multi-peak and skewed distributions, kernel density estimation directly obtains its probability distribution from the samples; the bandwidth parameter h is used to control the smoothness of the kernel function, including:

[0045] (8);

[0046] in, The Gaussian function is chosen as the kernel function.

[0047] Step S22: Calculate the corresponding bandwidth for different distributed power output values ​​using an adaptive nonparametric kernel density estimation method, including introducing an adaptive bandwidth factor to obtain the following:

[0048] (9)

[0049] Where α is the sensitivity factor, which is taken as 0.5 in this paper; z i x is the output value of the distributed power source. i The number of times it appears; p(x) i x represents the output value of the distributed power source. i The probability of occurrence;

[0050] Step S23: Substitute equation (9) into equation (8) to obtain the adaptive nonparametric kernel density estimation formula, as shown in equation (10):

[0051] (10)

[0052] Furthermore, the cumulative distribution function of the distributed power output is obtained:

[0053] (11);

[0054] Finally, the output of various distributed power sources after clustering of the Dirichlet process hybrid model is fitted by adaptive nonparametric kernel density estimation.

[0055] Further, step S3 includes the following:

[0056] Step S31: Let Let be the distribution function of the random variable x, where t is a real number, and satisfy: ,

[0057] Then the function For the interval (-∞, +∞) The relationships between integrable functions of the real variable t and the distributional characteristic function of F include:

[0058] (12);

[0059] in, Let f(x) be the characteristic function of the random variable; f(x) is the probability density function of x.

[0060] Step S32: Take the natural logarithm of the characteristic function of equation (12) and expand its Maclaurin series in the neighborhood where t takes a smaller value, to obtain:

[0061] (13)

[0062] in, Let v be a semi-invariant of order v for a random variable; The remainder of the expansion;

[0063] Step S33: During power flow calculation, the disturbance of random variables is transferred to the system state variables; based on the voltage sensitivity relationship, a linearized relationship is established between the state variables, including node voltages and branch power flows, and the node injected power, resulting in:

[0064] (14);

[0065] in, and The baseline expected values ​​for active and reactive power are injected into the nodes;

[0066] in and These are the baseline expected values ​​for the active and reactive power transmitted by the line.

[0067] in and Inject random disturbances of active and reactive power into the nodes;

[0068] and For random disturbances in the active and reactive power of the branch;

[0069] in and These are the baseline expected values ​​for node voltage and phase angle;

[0070] in and Power flow equations for node injection and branch power;

[0071] in The Jacobian matrix obtained for deterministic power flow calculation; This is the sensitivity matrix; and These are the changes in node voltage and phase angle;

[0072] Step S34: Substitute the random perturbation values ​​of the nodal injected power into equation (14) to obtain the semi-invariants of each order:

[0073] (15);

[0074] The semi-invariants of each order are obtained by convolution calculation of state variables including node voltages and branch power flows.

[0075] Furthermore, step S3 also includes the following:

[0076] Step S35: The random variables of node injected power consist of load, conventional unit output, and distributed generation output, and the semi-invariant method is used to solve for its semi-invariants of each order, including:

[0077] Step S351: The method for solving the semi-invariants of the load includes the following:

[0078] Assuming the load follows a normal distribution, the first-order semi-invariant of the load is the expected value, the second-order semi-invariant is the variance, and the third-order and higher-order semi-invariants are zero, thus we obtain:

[0079] (16)

[0080] Step S352: The semi-invariant solution method for conventional units includes the following:

[0081] Let p be the probability that a generator unit is in the powered-on state, and 1-p be the probability that it is in the powered-off state; if there are a total of Q generator units in the distribution network, the probability that q of them are operating normally is p. q ,get:

[0082] (17)

[0083] The torques of the output power of Q distributed power units are as follows:

[0084] (18)

[0085] In the formula, This is the rated capacity of a conventional unit;

[0086] After obtaining the moments of each order through equations (17) to (18), the semi-invariants of the output power of the conventional unit are calculated through equation (15).

[0087] Step S354: The semi-invariant solution method for distributed power sources includes the following:

[0088] First, by combining the inaccurate Dirichlet model and adaptive nonparametric kernel density estimation, the output probability density function of distributed power sources under different categories is obtained;

[0089] Then, the output data of N distributed power sources are extracted using the Latin hypercube sampling method:

[0090] ;

[0091] In constant power factor control mode, the active and reactive power of the distributed power source are proportional, and the corresponding reactive power data is obtained:

[0092] ;

[0093] Finally, based on the raw moment theorem, the raw moments of each order of the distributed power source output are further calculated to obtain:

[0094] (19)

[0095] in, and The v-th order original moment of active and reactive power output for distributed generation;

[0096] The relationship between the raw moment and the semi-invariants is shown in equation (20). By calculating the raw moment, the semi-invariants of the distributed power source output are obtained, including:

[0097] (20);

[0098] Furthermore, after estimating the moment characteristics of the distributed power generation output random variable, its semi-invariants are derived and calculated using moments, resulting in:

[0099] ;(twenty one);

[0100] in, This is a combination of i distributed power source output data extracted from v-1 different distributed power source output data.

[0101] Furthermore, step S3 also includes the following:

[0102] Step S36: Let the expected value of random variable P be μ. P The standard deviation is σ P , through Standardize it to obtain the standardized random variable P'; calculate the probability density function and cumulative distribution function of P' using the type A series expansion, and obtain:

[0103] ;(twenty two);

[0104] ;(twenty three);

[0105] in, Let be the probability density function of a random variable that follows a standard normal distribution;

[0106] for The result of the Nth order derivative;

[0107] The coefficients of each term in the series expansion are obtained from equation (24):

[0108] ;(twenty four);

[0109] In the formula, For standardized random variables, the v-order semi-invariant;

[0110] Step S37: In summary, based on the above steps: First, calculate the v-th order semi-invariant of the random variable P. Then, using the linear property of semi-invariants, we obtain... Finally, substituting into equations (22) and (23), we obtain the standardized random variable P'. and ;

[0111] Furthermore, the standardized random variable P' and To obtain the distribution of the original random variable P, we perform destandardization. The calculation process is as follows:

[0112] (25);

[0113] (26);

[0114] The series expansion is based on the standard normal distribution, and uses the semi-invariants of the random variable to construct correction terms, thereby approximating its probability density function and cumulative distribution function.

[0115] Further, step S4 includes the following:

[0116] Step S41: The expression for the severity Q of the loss due to node voltage exceeding the limit and line power flow exceeding the limit is:

[0117] (27)

[0118] in, β is the loss amount; β is the amplification factor, used to adjust the sensitivity of the loss severity.

[0119] The severity of losses from voltage and power flow exceeding limits depends on the magnitude of the corresponding losses, and the calculation method is as follows:

[0120] (28)

[0121] in, The voltage limit exceedance loss severity; U is the node voltage value; and These are the per-unit values ​​for the upper and lower limits of the node voltage;

[0122] (29);

[0123] in, The voltage limit exceedance loss severity; L is the ratio of the actual active power of the branch to the rated active power;

[0124] Step S42: Construct an index based on distribution entropy theory to measure the degree of change in the probability distribution of node voltage, line power flow, etc., after random factors are added to the distribution network, and assess the operational risks caused by the distribution changes accordingly; the definition of distribution entropy includes:

[0125] (30)

[0126] in, is the distribution entropy at time t; x is the node voltage or branch power flow to be evaluated; The number of states for the state variables of node voltages or branch power flows; for The probability of the z-th state;

[0127] Step S43: Since the distribution entropy is symmetric, when the probability matrix... When the order of elements changes, the entropy value remains unchanged; furthermore, the distribution entropy is weighted based on the severity of the loss to construct a weighted distribution entropy index, resulting in:

[0128] ;(31);

[0129] in, Let z be the severity of the loss in the z-th state of the state variable;

[0130] As can be seen from equation (31), as the degree of state variable exceeding the limit intensifies and the dispersion of state distribution increases, the weighted distribution entropy index increases accordingly, which indicates that the operational risk faced by the system increases.

[0131] According to a second aspect of the present invention, the present invention proposes a distribution network risk assessment system based on a Dirichlet process hybrid model and a semi-invariant method, for performing a distribution network risk assessment method based on a Dirichlet process hybrid model and a semi-invariant method as described in any one of the present invention, characterized in that it includes the following:

[0132] The Dirichlet process hybrid module has nonparametric modeling capabilities, which can adaptively identify the data cluster structure and extract uncertain information without the need to preset the number of categories, and is used for cluster analysis and probability density estimation of distributed power sources.

[0133] The adaptive nonparametric kernel density estimation module is used to obtain the probability distribution of kernel density estimation based on the distribution characteristics of distributed power source output data.

[0134] The semi-invariant and series expansion module is used to perform probabilistic power flow calculations on distribution networks containing distributed generation sources, and to quantify the degree of exceeding limits of branch power flow and node voltage probability distribution based on distribution entropy, thereby realizing the risk assessment of distribution network operation.

[0135] The distributed generation distribution network risk assessment module is used to comprehensively consider the losses caused by node voltage exceeding limits and line power flow exceeding limits, and to quantitatively calculate the distribution network exceeding limit risk index accordingly. Based on the distribution entropy theory, an index is constructed to measure the degree of change in the probability distribution, including node voltage and line power flow, after random factors are connected to the distribution network, so as to assess the operational risks caused by distribution changes.

[0136] The present invention has the following advantages:

[0137] This invention proposes a distribution network risk assessment method and system based on a Dirichlet process hybrid model and a semi-invariant method. Compared to traditional power output modeling methods that use preset distributions or fixed cluster numbers, this invention achieves Bayesian nonparametric clustering through DPMM, avoiding fitting bias caused by preset cluster numbers, and combines adaptive kernel density estimation to improve the local characterization capability of wind power output probability distribution. Compared to probabilistic power flow analysis methods mainly based on Monte Carlo simulation, this invention uses semi-invariants and Gram-Charlier series expansion to quickly solve the probability distribution of node state variables and branch power flows, improving computational efficiency while ensuring the accuracy of the results approximating the Monte Carlo simulation method. Furthermore, compared to index systems that only characterize risk with the probability or magnitude of exceeding limits, this invention constructs a risk assessment index based on distribution entropy, which can measure the risk of exceeding limits of state variables such as voltage and power flow and the risk caused by the uncertainty of their probability distribution, thereby achieving a more comprehensive and effective quantitative assessment of distribution network operation risks in high wind power penetration scenarios. Attached Figure Description

[0138] Figure 1 This is a schematic diagram of the steps of the present invention.

[0139] Figure 2 This is a schematic diagram of the distribution network risk assessment method based on wind power output in an embodiment of the present invention. Detailed Implementation

[0140] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0141] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0142] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0143] like Figures 1 to 2 As shown, this invention proposes a distribution network risk assessment method and system based on a Dirichlet process hybrid model and a semi-invariant method, including the following:

[0144] In this invention, the Dirichlet process mixture model (DPMM) can be represented as DPMM.

[0145] In one embodiment of the present invention, wind power output is used as the system output, resulting in the following:

[0146] In one embodiment of the present invention, the Dirichlet process hybrid model includes the following:

[0147] Because wind power distribution often exhibits non-normal characteristics such as multi-peak and irregular shape, and its distribution structure and parameters are difficult to determine in advance, traditional modeling methods based on the normality assumption are difficult to accurately characterize its statistical regularity. DPMM has non-parametric modeling capabilities and can adaptively identify data cluster structure and extract uncertain information without pre-setting the number of categories. Therefore, it is suitable for cluster analysis and probability density estimation of wind power.

[0148] Step S11: Assume the observed data comes from a mixed distribution of several unknown categories. ;

[0149] Select wind power output data As data to be clustered;

[0150] Assume the data follows a set of parameters The distribution is given by the parameter , where n is the number of data points. Data points belonging to the same parameter are grouped into the same category. Therefore, the wind power output data x to be clustered is ultimately divided into k categories, where k < n, meaning the number of categories k is less than the total number of data points n.

[0151] In this process, the parameter φ is generated by a Dirichlet Process (DP). DP is a type of stochastic probability distribution process that can adaptively generate latent classes and assign classes to observed samples as the amount of data increases, without needing to pre-define the number of classes. The number of classes is determined by the data itself.

[0152] Step S12: Let G be a random probability distribution on a measure space.

[0153] The measure space is arbitrarily partitioned as: a = {a1, a2, …, a r},

[0154] Furthermore, set Following a Dirichlet distribution, we obtain the following:

[0155] ;(1);

[0156] Where α0 is a hyperparameter, and α0>0, used to represent the degree of dispersion of G; G0 is the baseline distribution.

[0157] This process can be represented as a Dirichlet process DP(α0, G0). Since the Dirichlet distribution is the conjugate prior of the multinomial distribution, when the prior is a Dirichlet distribution and the likelihood is a multinomial distribution, the posterior distribution is still a Dirichlet distribution, thus exhibiting clustering characteristics.

[0158] Step S13: For a Dirichlet process, if the observed values ​​are sampled from the random measure G... Then its posterior distribution satisfies the following:

[0159] (2);

[0160] Where P is the probability of occurrence; For observations Quantity; for The Dirac function; N is the total number of observations.

[0161] Step S14: Since the Dirichlet process cannot be directly sampled, the Chinese Restaurant Process (CRP) is used to construct the random probability distribution G. In this model, the restaurant is considered to have an infinite number of tables; let x be the i-th customer entering the restaurant. i The tables in the restaurant for customers to sit at are Representation. The baseline distribution G0 and parameters. Let x and y represent the parameters of the k-th table. i A customer enters the restaurant and records the table. The number of customers already seated is m k The i-th customer is proportional to m k The probability of sitting at the table Above, also proportional to The probability of a customer sitting at a new table is [not specified]. Therefore, the table allocation for customers can be represented as:

[0162] (3);

[0163] Step S15: Although the Dirichlet process has clustering properties, its clustering mainly depends on the parameter values ​​being completely consistent, making it difficult to classify observations with different values ​​but high similarity into the same class.

[0164] Therefore, the Dirichlet process can be extended to DPMM, and its definition can be expressed as:

[0165] (4);

[0166] The wind power output data is clustered using the DPMM constructed by CRP. The DPMM model based on CRP yields the following results:

[0167] (5);

[0168] in, It follows a Gaussian distribution; For the mean and variance.

[0169] Step S16: Further derive the following:

[0170] For an existing cluster k, given the parameters of cluster k, sample x i The conditional probability can be expressed as follows:

[0171] (6);

[0172] in, and The posterior mean and variance of cluster k are obtained by updating the data based on the observation data; is the updated number of samples for cluster k.

[0173] The conditional probability of the new cluster k+1 can be expressed as follows:

[0174] (7);

[0175] in, and Let be the prior mean and variance of the new cluster; Count the prior samples for the new cluster.

[0176] Step S17: After calculating the conditional probability, the Gibbs sampling algorithm is used to update the class assignment for each sample. Through multiple iterations, the optimal class assignment result is finally converged.

[0177] In one embodiment of the present invention, the adaptive nonparametric kernel density estimation model includes the following:

[0178] Step S21: Given the complex distribution characteristics of wind power output data, such as multi-peak and skewed distribution, kernel density estimation does not require a pre-defined distribution form and can directly characterize its probability distribution based on the samples. The bandwidth parameter h controls the smoothness of the kernel function, and its expression is shown below.

[0179] (8);

[0180] in, The kernel function is a Gaussian function, which is chosen as the kernel function.

[0181] Step S22: The selection of bandwidth is crucial to the accuracy of distribution fitting. Too small a bandwidth can make the estimation results overly sensitive, leading to overfitting, while too large a bandwidth weakens the characterization of distribution details. Traditional KDE uses a fixed bandwidth, which cannot adaptively adjust based on local density changes in wind power output data, potentially causing overfitting or underfitting in both concentrated and dispersed data points. To address these issues, an adaptive nonparametric kernel density estimation method is proposed to calculate the corresponding bandwidth for different wind power output values. The specific method is as follows.

[0182] Introducing an adaptive bandwidth factor yields:

[0183] (9)

[0184] Where α is the sensitivity factor, which is taken as 0.5 in this paper; z i x is the wind power output value i The number of times it appears; p(x) i (x) represents the wind power output value. i The probability of occurrence.

[0185] Step S23: Substitute equation (9) into equation (8) to obtain the adaptive nonparametric kernel density estimation formula, as shown in equation (10):

[0186] (10)

[0187] The cumulative distribution function of wind power output is further obtained as follows:

[0188] (11);

[0189] Finally, the wind power output of various types after clustering of the Dirichlet process hybrid model can be fitted by adaptive nonparametric kernel density estimation.

[0190] In one embodiment of the present invention, the risk assessment method considering distributed wind power includes the following:

[0191] We employ semi-invariants and Gram-Charlier series expansion to perform probabilistic power flow calculations on distribution networks containing distributed wind power, and quantify the extent to which branch power flow and node voltage probability distributions exceed limits based on distribution entropy, thereby achieving risk assessment of distribution network operation.

[0192] Step S31: Semi-invariants are a numerical characteristic of random variables, often used to quantify downside risk of deviation from expected values. They are defined as follows: Let... Let be the distribution function of the random variable x, where t is a real number, and satisfy . Then the function For the interval (-∞, +∞) The relationships between integrable functions of the real variable t and the distributional characteristic function of F include:

[0193] (12);

[0194] in, Let f(x) be the characteristic function of the random variable; f(x) is the probability density function of x.

[0195] Step S32: Take the natural logarithm of the characteristic function of equation (12) and expand its Maclaurin series in the neighborhood where t takes a smaller value, and you can get the following expression:

[0196] (13)

[0197] in, Let v be a semi-invariant of order v for a random variable; This is the remainder term in the expansion.

[0198] Step S33: When performing power flow calculations, it is necessary to transfer the disturbances of random variables into the system state variables. Based on the voltage sensitivity relationship, a linearized relationship can be established between state variables such as node voltage and branch power flow and node injected power, as shown below:

[0199] (14);

[0200] in, and The baseline expected values ​​for active and reactive power are injected into the nodes;

[0201] in and These are the baseline expected values ​​for the active and reactive power transmitted by the line.

[0202] in and Inject random disturbances of active and reactive power into the nodes;

[0203] and For random disturbances in the active and reactive power of the branch;

[0204] in and These are the baseline expected values ​​for node voltage and phase angle;

[0205] in and Power flow equations for node injection and branch power;

[0206] in The Jacobian matrix obtained for deterministic power flow calculation; This is the sensitivity matrix; and These represent the changes in node voltage and phase angle.

[0207] Step S34: Substitute the random disturbance value of the injected power at the node into equation (14), and calculate the semi-invariants of each order of state variables such as node voltage and branch power flow through convolution, including:

[0208] (15);

[0209] Step S35: The random variables of node injected power consist of load, conventional unit output, and wind power output, and the semi-invariant method is used to solve for its semi-invariants of each order. The specific process includes:

[0210] Step S351: The method for solving the semi-invariants of the load includes the following:

[0211] Considering the prediction error and randomness of the load, we assume it follows a normal distribution. In this case, the first-order semi-invariant of the load is the expected value, the second-order semi-invariant is the variance, and the third-order and higher-order semi-invariants are zero, as specifically expressed below.

[0212] (16)

[0213] Step S352: The semi-invariant solution method for conventional units includes the following:

[0214] Traditional generator sets typically have only two states: running and shut down. Assume the probability of a generator set being running is p, and the probability of it being shut down is 1-p. If there are Q generator sets in a distribution network, the probability that q of them are running normally is p. q Therefore, we can draw the following conclusion:

[0215] (17)

[0216] The torques of the output power of the Q wind turbine are as follows.

[0217] (18)

[0218] In the formula, This refers to the rated capacity of a conventional unit.

[0219] After obtaining the moments of each order through equations (17) to (18), the semi-invariants of the output power of the conventional unit can be calculated further through equation (15).

[0220] Step S354: The method for solving the semi-invariants of wind power includes the following:

[0221] To mitigate the impact of the randomness of wind power output on its distribution, firstly, an inexact Dirichlet model and adaptive nonparametric kernel density estimation are combined to obtain the probability density function of wind power output under different categories. Then, N wind power output data points are extracted using the Latin hypercube sampling method.

[0222] .

[0223] Under constant power factor control mode, the active and reactive power of wind power are directly proportional, thus allowing the acquisition of corresponding reactive power data.

[0224] .

[0225] Finally, based on the original moment theorem, the original moments of each order of wind power output are further calculated.

[0226] (19)

[0227] in, and The v-th order origin moment represents the active and reactive power output of wind power.

[0228] The relationship between the moment of origin and the semi-invariants is shown in equation (20). By calculating the moment of origin, the semi-invariants of wind power output can be further obtained, including:

[0229] (20);

[0230] Furthermore, after estimating the moment characteristics of each order of the random variable of wind power output, its semi-invariants are derived and calculated from the moments, as follows.

[0231] ;(twenty one);

[0232] in, This is a combination of i wind power output data points extracted from v-1 different wind power output data points.

[0233] In one embodiment of the present invention, the Cornish-Charlier series expansion method includes the following:

[0234] The Gram-Charlier series expansion uses the standard normal distribution as a benchmark and constructs correction terms using the semi-invariants of the random variable to approximate its probability density function and cumulative distribution function.

[0235] Step S41: Let the expected value of random variable P be μ. P The standard deviation is σ P , through Standardizing the variable yields the standardized random variable P'. Using a Gram-Charlier series expansion of type A, the probability density function and cumulative distribution function of P' can be further derived, as expressed below.

[0236] ;(twenty two);

[0237] ;(twenty three);

[0238] in, Let be the probability density function of a random variable that follows a standard normal distribution;

[0239] for The result of the Nth order derivative;

[0240] The coefficients of the Gram-Charlier series expansion are calculated by equation (24).

[0241] ;(twenty four);

[0242] In the formula, Let v be a semi-invariant of the standardized random variable.

[0243] Step S42: In summary, based on the above steps: First, calculate the v-th order semi-invariant of the random variable P. Then, using the linear property of semi-invariants, we obtain... Finally, substituting these equations into equations (22) and (23), we can obtain the standardized random variable P'. and .

[0244] In addition, the standardized random variable P' also needs to be... and To obtain the distribution of the original random variable P, we perform destandardization and restoration. The calculation process is shown in the following formula.

[0245] (25);

[0246] (26);

[0247] In one embodiment of the present invention, the risk assessment of a distribution network containing distributed wind power includes the following:

[0248] To comprehensively assess the operational risks of distribution networks including wind power, the losses caused by node voltage exceeding limits and line power flow exceeding limits are considered together, and the distribution network exceeding limit risk index is quantitatively calculated accordingly. Its expression is as follows.

[0249] In one embodiment of the present invention, the severity of the loss includes the following:

[0250] Step S51: The severity Q of the loss due to node voltage exceeding the limit and line power flow exceeding the limit can be calculated using the following formula:

[0251] (27)

[0252] In the formula, β is the loss amount; β is the amplification factor, used to adjust the sensitivity of the loss severity, and is set to 82.422.

[0253] The severity of losses from voltage and power flow exceeding limits depends on the magnitude of the corresponding losses, and the calculation method is as follows:

[0254] (28)

[0255] in, The voltage limit exceedance loss severity; U is the node voltage value; and The per-unit values ​​for the upper and lower limits of the node voltage are 1.05 and 0.95, respectively.

[0256] (29)

[0257] in, The voltage over-limit loss severity; L is the ratio of the actual active power of the branch to the rated active power.

[0258] In one embodiment of the present invention, the weighted distribution entropy includes the following:

[0259] Step S52: Construct an index based on distribution entropy theory to measure the degree of change in the probability distribution of node voltage, line power flow, etc., after random factors are connected to the distribution network, and assess the operational risks caused by the distribution changes accordingly. The definition of distribution entropy is as follows.

[0260] (30)

[0261] in, is the distribution entropy at time t; x is the node voltage or branch power flow to be evaluated; The number of states for the state variables of node voltages or branch power flows; for The probability of the z-th state.

[0262] Step S53: Since the distribution entropy is symmetric, when the probability matrix... When the order of elements in the distribution changes, the entropy value remains unchanged. As a result, in probabilistic power flow simulations, if the probability distributions of state variables concentrated in regions of smaller and larger losses are numerically the same, the corresponding distribution entropy results will also be the same. However, the operational risks in the two scenarios are clearly different, which is inconsistent with the actual operating characteristics of the power grid. Therefore, a weighted distribution entropy index is constructed by weighting the distribution entropy based on the severity of the losses, and its calculation formula is as follows.

[0263] (31);

[0264] in, Let z be the severity of the loss in the z-th state of the state variable.

[0265] As can be seen from equation (31), as the degree of state variable exceeding the limit intensifies and the dispersion of state distribution increases, the weighted distribution entropy index increases accordingly, which indicates that the operational risk faced by the system increases.

[0266] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

[0267] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A distribution network risk assessment method based on a Dirichlet process hybrid model and a semi-invariant method, characterized in that, Includes the following: A Dirichlet process mixture model is introduced to perform Bayesian nonparametric clustering on the output samples of distributed generation, and an adaptive kernel density estimation is used to fit the probability density within each cluster to obtain the probability distribution model of distributed generation output. To address the random fluctuation characteristics of distributed generation and load in distribution networks, a probabilistic power flow solution method combining semi-invariants and series expansion is constructed. This method enables the description of the probability distribution of node state variables and branch power flow, while providing basic probabilistic power flow data support for subsequent risk assessment. Based on the theory of distributed entropy, a risk assessment index for distribution networks is constructed to characterize the risk of exceeding limits of state variables, including voltage and power flow, and further to obtain the risk caused by the uncertainty of the probability distribution of state variables, thereby realizing the risk assessment of distribution networks.

2. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 1, characterized in that, The aforementioned distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method further includes the following steps: Step S1: Establish a Dirichlet process hybrid model to adaptively identify the data cluster structure and extract uncertain information without pre-setting the number of categories, thereby realizing cluster analysis and probability density estimation of distributed power sources. Step S2: Establish an adaptive nonparametric kernel density estimation model, including obtaining the probability distribution of kernel density estimation based on the distribution characteristics of distributed power generation output data; Step S3: Use semi-invariants and series expansion to perform probabilistic power flow calculations on distribution networks containing distributed generation sources, and quantify the degree of exceeding limits of branch power flow and node voltage probability distribution based on distribution entropy, thereby realizing the risk assessment of distribution network operation. Step S4: Conduct a risk assessment of the distribution network including distributed generation, including comprehensively considering the losses caused by node voltage exceeding limits and line power flow exceeding limits, and quantitatively calculate the distribution network exceeding limit risk index accordingly; construct an index based on distribution entropy theory to measure the degree of change in the probability distribution including node voltage and line power flow after random factors are connected to the distribution network, so as to assess the operational risks caused by distribution changes.

3. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 2, characterized in that, Step S1 includes the following: Step S11: Assume the observed data comes from a mixed distribution of several unknown categories. ; Selecting distributed power generation output data As data to be clustered; Suppose the data to be clustered follows a set of parameters The distribution of data is defined by n, where n is the number of data points. Data belonging to the same parameter φ are grouped into the same category. The distributed power output data x to be clustered is divided into k categories, where k < n, indicating that the number of categories k is less than the total number of data points n. Step S12: Let G be a random probability distribution on a measure space. The measure space is arbitrarily partitioned as: a = {a1, a2, …, a r }, Furthermore, set Following a Dirichlet distribution, we obtain the following: ；(1)； Where α0 is a hyperparameter, and α0>0, used to represent the degree of dispersion of G; G0 is the baseline distribution; Step S13: For a Dirichlet process, if the observed values ​​are sampled from the random measure G... Then its posterior distribution satisfies the following: ；(2)； Where P is the probability of occurrence; For observations Quantity; for The Dirac function; N is the total number of observations.

4. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 3, characterized in that, Step S1 also includes the following: Step S14: Construct the random probability distribution G using the Chinese restaurant process, including: Consider the restaurant as having an infinite number of tables; let x be the i-th customer entering the restaurant. i The tables in the restaurant for customers to sit at are Representation; baseline distribution G0 and parameters Let x and y represent the parameters of the k-th table; x and y represent the parameters of the x-th table. i A customer enters the restaurant and records the table. The number of customers already seated is m k The i-th customer is proportional to m k The probability of sitting at the table Above, also proportional to The probability of a customer sitting at a new table is represented as: ；(3)； Step S15: Extend the Dirichlet process into a Dirichlet process hybrid model, resulting in: ；(4)； Clustering distributed power source output data using a Dirichlet process hybrid model constructed from the Chinese restaurant process yields the following results: ；(5)； in, It follows a Gaussian distribution; The mean and variance are given. Step S16: For an existing cluster k, given the parameters of cluster k, sample x i Conditional probabilities include: ；(6)； in, and The posterior mean and variance of cluster k are obtained by updating the data based on the observation data; Let k be the updated number of samples for cluster k. The expression for the conditional probability of the new cluster k+1 is: ；(7)； in, and Let be the prior mean and variance of the new cluster; Count the prior samples for the new cluster; Step S17: After calculating the conditional probability, the Gibbs sampling algorithm is used to update the class assignment for each sample. Through multiple iterations, the optimal class assignment result is finally converged.

5. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 4, characterized in that, Step S2 includes the following: Step S21: Based on the distributed power output data, which exhibits distribution characteristics including multi-peak and skewed distributions, kernel density estimation directly obtains its probability distribution from the samples; the bandwidth parameter h is used to control the smoothness of the kernel function, including: ；(8)； in, The Gaussian function is chosen as the kernel function. Step S22: Calculate the corresponding bandwidth for different distributed power output values ​​using an adaptive nonparametric kernel density estimation method, including introducing an adaptive bandwidth factor to obtain the following: ；(9)； Where α is the sensitivity factor, which is taken as 0.5 in this paper; z i x is the output value of the distributed power source. i The number of times it appears; p(x) i x represents the output value of the distributed power source. i The probability of occurrence; Step S23: Substitute equation (9) into equation (8) to obtain the adaptive nonparametric kernel density estimation formula, as shown in equation (10): ；(10)； Furthermore, the cumulative distribution function of the distributed power output is obtained: ；(11)； Finally, the output of various distributed power sources after clustering of the Dirichlet process hybrid model is fitted by adaptive nonparametric kernel density estimation.

6. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 5, characterized in that, Step S3 includes the following: Step S31: Let Let be the distribution function of the random variable x, where t is a real number, and satisfy: , Then the function For the interval (-∞, +∞) The relationships between integrable functions of the real variable t and the distributional characteristic function of F include: ；(12)； in, Let f(x) be the characteristic function of the random variable; f(x) is the probability density function of x. Step S32: Take the natural logarithm of the characteristic function of equation (12) and expand its Maclaurin series in the neighborhood where t takes a smaller value, to obtain: ；(13)； in, Let v be a semi-invariant of order v for a random variable; The remainder of the expansion; Step S33: During power flow calculation, the disturbance of random variables is transferred to the system state variables; based on the voltage sensitivity relationship, a linearized relationship is established between the state variables, including node voltages and branch power flows, and the node injected power, resulting in: ；(14)； in, and The baseline expected values ​​for active and reactive power are injected into the nodes; in and These are the baseline expected values ​​for the active and reactive power transmitted by the line. in and Inject random disturbances of active and reactive power into the nodes; and For random disturbances in the active and reactive power of the branch; in and These are the baseline expected values ​​for node voltage and phase angle; in and Power flow equations for node injection and branch power; in The Jacobian matrix obtained for deterministic power flow calculation; This is the sensitivity matrix; and These are the changes in node voltage and phase angle; Step S34: Substitute the random perturbation values ​​of the nodal injected power into equation (14) to obtain the semi-invariants of each order: ；(15)； The semi-invariants of each order are obtained by convolution calculation of state variables including node voltages and branch power flows.

7. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 6, characterized in that, Step S3 also includes the following: Step S35: The random variables of node injected power consist of load, conventional unit output, and distributed generation output, and the semi-invariant method is used to solve for its semi-invariants of each order, including: Step S351: The method for solving the semi-invariants of the load includes the following: Assuming the load follows a normal distribution, the first-order semi-invariant of the load is the expected value, the second-order semi-invariant is the variance, and the third-order and higher-order semi-invariants are zero, thus we obtain: ；(16)； Step S352: The semi-invariant solution method for conventional units includes the following: Let p be the probability that a generator unit is in the powered-on state, and 1-p be the probability that it is in the powered-off state; if there are a total of Q generator units in the distribution network, the probability that q of them are operating normally is p. q ,get: ；(17)； The torques of the output power of Q distributed power units are as follows: ；(18)； In the formula, This is the rated capacity of a conventional unit; After obtaining the moments of each order through equations (17) to (18), the semi-invariants of the output power of the conventional unit are calculated through equation (15). Step S354: The semi-invariant solution method for distributed power sources includes the following: First, by combining the inaccurate Dirichlet model and adaptive nonparametric kernel density estimation, the output probability density function of distributed power sources under different categories is obtained; Then, the output data of N distributed power sources are extracted using the Latin hypercube sampling method: ； Under constant power factor control mode, the active and reactive power of the distributed power source are proportional, and the corresponding reactive power data is obtained. Finally, based on the raw moment theorem, the raw moments of each order of the distributed power source output are further calculated to obtain: ；(19)； in, and The v-th order original moment of active and reactive power output for distributed generation; The relationship between the raw moment and the semi-invariants is shown in equation (20). By calculating the raw moment, the semi-invariants of the distributed power source output are obtained, including: ；(20)； Furthermore, after estimating the moment characteristics of the distributed power output random variable, its semi-invariants are derived and calculated using moments, resulting in: ；(21)； in, This is a combination of i distributed power source output data extracted from v-1 different distributed power source output data.

8. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 7, characterized in that, Step S3 also includes the following: Step S36: Let the expected value of random variable P be μ. P The standard deviation is σ P , through Standardize it to obtain the standardized random variable P'; calculate the probability density function and cumulative distribution function of P' using the type A series expansion, and obtain: ；(22)； ；(23)； in, Let be the probability density function of a random variable that follows a standard normal distribution; for The result of the Nth order derivative; The coefficients of each term in the series expansion are obtained from equation (24): ；(24)； In the formula, For standardized random variables, the v-th order semi-invariant; Step S37: In summary, based on the above steps: First, calculate the v-th order semi-invariant of the random variable P. Then, using the linear property of semi-invariants, we obtain... Finally, substituting into equations (22) and (23), we obtain the standardized random variable P'. and ; Furthermore, the standardized random variable P' and To obtain the distribution of the original random variable P, we perform destandardization. The calculation process is as follows: ；(25)； ；(26)； The series expansion is based on the standard normal distribution, and uses the semi-invariants of the random variable to construct correction terms, thereby approximating its probability density function and cumulative distribution function.

9. The distribution network risk assessment method based on the Dirichlet process hybrid model and semi-invariant method according to claim 8, characterized in that, Step S4 includes the following: Step S41: The expression for the severity Q of the loss due to node voltage exceeding the limit and line power flow exceeding the limit is: ；(27)； in, β is the loss amount; β is the amplification factor, used to adjust the sensitivity of the loss severity. The severity of losses from voltage and power flow exceeding limits depends on the magnitude of the corresponding losses, and the calculation method is as follows: ；(28)； in, The voltage limit exceedance loss severity; U is the node voltage value; and These are the per-unit values ​​for the upper and lower limits of the node voltage; ；(29)； in, The voltage limit exceedance loss severity; L is the ratio of the actual active power of the branch to the rated active power; Step S42: Construct an index based on distribution entropy theory to measure the degree of change in the probability distribution of node voltage, line power flow, etc., after random factors are added to the distribution network, and assess the operational risks caused by the distribution changes accordingly; the definition of distribution entropy includes: ；(30)； in, is the distribution entropy at time t; x is the node voltage or branch power flow to be evaluated; The number of states for the state variables of node voltages or branch power flows; for The probability of the z-th state; Step S43: Since the distribution entropy is symmetric, when the probability matrix... When the order of elements changes, the entropy value remains unchanged; furthermore, the distribution entropy is weighted based on the severity of the loss to construct a weighted distribution entropy index, resulting in: ；(31)； in, Let z be the severity of the loss in the z-th state of the state variable; As can be seen from equation (31), as the degree of state variable exceeding the limit intensifies and the dispersion of state distribution increases, the weighted distribution entropy index increases accordingly, which indicates that the operational risk faced by the system increases.

10. A distribution network risk assessment system based on a Dirichlet process hybrid model and a semi-invariant method, used to execute a distribution network risk assessment method based on a Dirichlet process hybrid model and a semi-invariant method as described in any one of claims 1 to 9, characterized in that, Includes the following: The Dirichlet process hybrid module has nonparametric modeling capabilities, which can adaptively identify the data cluster structure and extract uncertain information without the need to preset the number of categories, and is used for cluster analysis and probability density estimation of distributed power sources. The adaptive nonparametric kernel density estimation module is used to obtain the probability distribution of kernel density estimation based on the distribution characteristics of distributed power source output data. The semi-invariant and series expansion module is used to perform probabilistic power flow calculations on distribution networks containing distributed generation sources, and to quantify the degree of exceeding limits of branch power flow and node voltage probability distribution based on distribution entropy, thereby realizing the risk assessment of distribution network operation. The distributed generation distribution network risk assessment module is used to comprehensively consider the losses caused by node voltage exceeding limits and line power flow exceeding limits, and to quantitatively calculate the distribution network exceeding limit risk index accordingly. Based on the distribution entropy theory, an index is constructed to measure the degree of change in the probability distribution, including node voltage and line power flow, after random factors are connected to the distribution network, so as to assess the operational risks caused by distribution changes.

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