Static risk assessment method and device for power distribution network system

Abstract

The invention discloses a static risk assessment method and equipment for a power distribution network system, and belongs to the technical field of power systems. The method comprises the following steps: carrying out standardization processing on an uncertainty input variable in a power distribution network system to obtain a standard input variable; polynomial chaos expansion is carried out on the output of the power distribution network system, sparse processing is carried out on a primary function of polynomial chaos expansion, numerical integration is carried out on a standard input variable to calculate a polynomial chaos expansion coefficient, and an obtained polynomial chaos expansion formula is used as a high-dimensional agent model of the output of the power distribution network system; and performing static risk assessment on the power distribution network system based on the high-dimensional agent model. According to the method, sparse processing is carried out on the polynomial basis function, the dimension of the basis function is controlled, and then the polynomial coefficient is calculated through numerical integration, so that the overall calculation efficiency is remarkably improved under the same precision requirement, and the requirement of carrying out real-time evaluation on the static risk of a novel intelligent power distribution network system is met.

Description

Technical Field

[0001] The invention relates to a method and equipment for evaluating static risk of a distribution network system, and belongs to the technical field of power systems. Background Art

[0002] With the rapid growth of the proportion of renewable energy power generation and the widespread access to distributed resources, the operation mode of the distribution network is undergoing profound changes. However, the intermittent and random nature of renewable energy such as wind power and photovoltaics, coupled with the dynamic changes in load demand, makes the distribution network face significant operational risks and stability challenges under high penetration conditions. The increase in uncertainty factors makes it difficult for traditional deterministic analysis methods to fully reflect the complexity of the system's operating status. Efficient and accurate risk assessment technology is urgently needed to provide a scientific basis for the dispatch optimization and safety assurance of the distribution network.

[0003] Existing risk assessment methods are mainly divided into two categories: deterministic assessment and probabilistic risk assessment. Deterministic assessment methods ignore the probabilistic characteristics of the operating state by assuming extreme conditions, and the assessment results are conservative. Probabilistic risk assessment methods can provide a more comprehensive description of the system state through probabilistic power flow analysis. However, the traditional probabilistic methods represented by Monte Carlo Simulation (MCS) have extremely high computational costs and are difficult to meet real-time requirements. Although subsequent techniques such as variance reduction and approximate expansion have been proposed, when the dimension is large, the full tensor product will cause the number of configuration points to grow exponentially, forming a "dimensionality disaster" in high-dimensional scenarios. In other words, traditional polynomial chaos expansion (PCE) often faces the dilemma of a simultaneous surge in the number of basis functions and the number of integration points under high-dimensional random variables, resulting in a significant decrease in overall computational efficiency. Therefore, how to balance accuracy and efficiency has become a core issue that needs to be urgently addressed in distribution network risk assessment technology. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method and device for static risk assessment of a distribution network system, which solves the problem of a synchronous surge in the number of basis functions and the number of integration points faced by traditional PCE under high-dimensional random variables.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0006] In a first aspect, the present invention provides a method for static risk assessment of a distribution network system, comprising:

[0007] Standardize the uncertain input variables in the distribution network system to obtain standard input variables that obey the preset probability distribution;

[0008] Based on the distribution type of the standard input variables, a polynomial chaos expansion is performed on the output of the distribution network system, a basis function of the polynomial chaos expansion is sparsely processed, the standard input variables are numerically integrated to calculate the polynomial chaos expansion coefficients, and the obtained polynomial chaos expansion is used as a high-dimensional proxy model of the output of the distribution network system;

[0009] Based on the high-dimensional agent model, a probabilistic power flow calculation is performed on the distribution network system to obtain statistical characteristics of output variables of the distribution network system;

[0010] Based on the statistical characteristics of the output variables of the distribution network system, a static risk assessment is performed on the distribution network system.

[0011] Furthermore, the preset probability distribution is a standard normal distribution; the formula for standardizing the uncertain input variables in the distribution network system is:

[0012] in, Enter variables for uncertainty The cumulative distribution function of For about The inverse cumulative distribution function of the standard normal distribution is Standard input variables The standard distribution function of .

[0013] Furthermore, the sparse processing of the basis functions of the polynomial chaotic expansion includes:

[0014] The polynomial chaos expansion of the distribution network system output is:

[0015]

[0016] In the formula, Output of the distribution network system, Input variables for multidimensional criteria, is the number of standard input variables, is a multiple index, is the set of multiple exponentials of the polynomial, is the polynomial chaos expansion coefficient, For about The polynomial basis function of is expressed as:

[0017]

[0018] In the formula, Standard input variables The order of Standard input variables The order of The basis functions of

[0019] The hyperbolic truncation method is used to perform hyperbolic truncation on the polynomial chaotic expansion output by the distribution network system to obtain the hyperbolic truncation polynomial chaotic expansion, which is specifically:

[0020] In the hyperbolic truncation process, we introduce Norm vs. Multiple Exponential Imposing restrictions:

[0021]

[0022] In the formula, For multiple indexes of norm, where ; The standard input variable The order of As the base number, The norm is the power calculation of the exponent, The preset maximum truncation order.

[0023] Furthermore, the standard input variable is a multidimensional standard input variable; the numerical integration is a multidimensional numerical integration; the calculation of polynomial chaos expansion coefficients by numerical integration of the standard input variable includes:

[0024] Get multi-dimensional integral points;

[0025] Based on the multi-dimensional integration points, numerical integration is performed to approximately calculate the polynomial chaos expansion coefficients, and the calculation formula is:

[0026]

[0027] In the formula, is the polynomial chaos expansion coefficient, is the normalization coefficient, is the number of groups of multidimensional integration points, For the Set of multidimensional integration points, For the The weights of the multidimensional integration points, For the The calculation results of the polynomial chaos expansion at the multidimensional integration points of the group, For the Polynomial basis functions at the multidimensional integration points.

[0028] Furthermore, the multidimensional integration points are obtained by combining the one-dimensional integration points of each standard input variable; wherein the one-dimensional integration points of the standard input variables are obtained by the Clenshaw-Curtis integration formula, specifically:

[0029] In the interval In the interval, the midpoint 0 is taken as the initial point, and integration points are gradually added on both sides of the initial point according to the order of Clenshaw-Curtis integration. The number of integration points is calculated as follows:

[0030]

[0031] In the formula, is the order of the Clenshaw-Curtis integration, is the number of integration points corresponding to the order.

[0032] Furthermore, the one-dimensional integration points of each standard input variable are combined in the following manner: the Smolyak sparse grid technique is used to perform linear combinations of tensor products on integration points of different dimensions to construct a high-dimensional sparse grid.

[0033] Furthermore, after calculating the polynomial chaos expansion coefficients by numerical integration of the standard input variables, the method further includes: reducing the polynomial chaos expansion coefficients corresponding to some polynomial basis functions to zero by using a Lasso regression algorithm, specifically:

[0034] Establish the optimization objective function of Lasso regression:

[0035]

[0036] In the formula, is the polynomial chaos expansion coefficient vector, The corresponding minimization of the objective function , is the number of groups of multidimensional integration points, For the The polynomial basis functions at the multidimensional integration points of the group, For the The real output of the distribution network system at the group integration point; is the regularization coefficient; is a multiple index, is the set of multiple exponentials of the polynomial, is the absolute value of the polynomial chaos expansion coefficient;

[0037] Using the cross-validation method, Select the best performing candidate from the candidate set value.

[0038] Furthermore, based on the statistical characteristics of the output variables of the distribution network system, a static risk assessment is performed on the distribution network system, including:

[0039] Based on the statistical characteristics of the output variables of the distribution network system, a cumulative distribution function of the node voltage and a cumulative distribution function of the branch transmission power are obtained;

[0040] The probability of each node voltage exceeding the limit is obtained according to the cumulative distribution function of the node voltage:

[0041]

[0042] In the formula, For Node The voltage amplitude, For Node The upper limit of the voltage amplitude is For Node The lower limit of the voltage amplitude is for Greater than The probability of for Less than The probability of and Node The probability of the voltage exceeding the upper limit and the probability of exceeding the lower limit; for The cumulative distribution function of for The cumulative distribution function of

[0043] An exponential function is used to quantify the voltage limit:

[0044]

[0045] In the formula, For about An exponential function of is an exponential function with the natural constant e as base;

[0046] Calculate the risk of node voltage exceeding the limit:

[0047]

[0048] In the formula, For Node The voltage over-limit risk value;

[0049] The branch overload probability is obtained according to the cumulative distribution function of the branch transmission power:

[0050]

[0051] In the formula, For branch The transmission power, For branch The upper limit power value allowed to be carried, For branch The overload probability, for Greater than The probability of for The cumulative distribution function of

[0052] An exponential function is used to quantify the severity of branch overload:

[0053]

[0054] Calculate the branch overload risk:

[0055]

[0056] In the formula, For about An exponential function of For branch overload risk value.

[0057] Furthermore, the static risk assessment of the distribution network system also includes: calculating the comprehensive risk index of the distribution network system, and the calculation formula is:

[0058]

[0059] In the formula, is the first comprehensive risk indicator, is the second comprehensive risk indicator, is the number of nodes in the distribution network system, is the number of branches in the distribution network system; is the first weight coefficient, is the second weight coefficient, .

[0060] In a second aspect, the present invention provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the static risk assessment method for the distribution network system described in the first aspect.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] (1) The static risk assessment method for distribution network system provided by the present invention first performs sparse processing on the basis functions of polynomial chaos expansion to control the dimension of the basis functions and reduce the amount of subsequent calculations. After determining the candidate basis function set, the polynomial chaos expansion coefficients are calculated by numerically integrating the standard input variables, thereby significantly improving the overall calculation efficiency under the same accuracy requirements, and meeting the needs of real-time assessment of the static risks of new distribution network systems.

[0063] (2) The static risk assessment method for distribution network system provided by the present invention is introduced into the multi-exponential space by the hyperbolic truncation method. norm constraint, and set , only the multi-exponential combination terms that satisfy the norm less than or equal to the preset maximum truncation order are retained, which can effectively suppress the number of high-dimensional and high-order cross terms when constructing the proxy model. Most high-dimensional coupling terms will be excluded, effectively reducing the computational complexity;

[0064] (3) The static risk assessment method for the distribution network system provided by the present invention adopts the Smolyak sparse grid technology to replace the traditional full tensor product. By differentially combining one-dimensional integration points in multi-dimensional space, most of the "high-order × high-order" interaction terms are skipped, which greatly reduces the number of multi-dimensional integration points and the computational burden, effectively solving the problem of explosive growth in the number of integration points in high-dimensional scenarios.

[0065] (4) The static risk assessment method for the distribution network system provided by the present invention adopts the Lasso regression algorithm, which minimizes the objective function and imposes a penalty on the calculated polynomial chaotic expansion coefficients to sparse the expansion coefficients and find the optimal solution, thereby further achieving effective simplification of the basis function and improving the calculation efficiency;

[0066] (5) The static risk assessment method for the distribution network system of the present invention can not only accurately quantify the probability distribution of node voltage and branch power, but also effectively assess the risk of over-limit and overload, providing a scientific basis for the safety assessment and dispatching decision-making of the new distribution network system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the static risk assessment method of the distribution network system in the present invention;

[0068] Figure 2 It is a comparison diagram of the voltage amplitude probability density function PDF and cumulative distribution function CDF curves of the node 33 in the IEEE-118 node power distribution system in Example 4 of the present invention;

[0069] Figure 3 It is a comparison diagram of the active power probability density function PDF and cumulative distribution function CDF curves of branch 10-11 in the IEEE-118 node power distribution system in Example 4 of the present invention. DETAILED DESCRIPTION

[0070] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices. The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments.

[0071] At present, the smart distribution network system characterized by the grid connection of distributed wind and solar power generation and the access of new re-electrification loads has become an important form of connecting green energy production and low-carbon consumption. However, the high proportion of renewable energy generation is intermittent, and the large-scale heterogeneous power loads (electric vehicles, air conditioners, etc.) are random, which will have a significant impact on the operation of the distribution network. Therefore, it is necessary to analyze the propagation process of source-load uncertainty, study the quantification method of distribution network system operation uncertainty, and realize the static risk assessment of the distribution network system to ensure the safe and economic operation of the smart distribution network system.

[0072] Example 1

[0073] refer to Figure 1 This embodiment provides a method for static risk assessment of a distribution network system, including:

[0074] Step 1: Standardize the uncertain input variables in the distribution network system to obtain standard input variables that obey the preset probability distribution.

[0075] Specifically, the uncertain input variables in the distribution network system include: new energy output and load fluctuations. Since different uncertain input variables may follow different distribution types, this embodiment introduces an iso-probabilistic transform (IPT) to standardize the uncertain input variables with non-standard distribution and map them to a standard distribution.

[0076] In some specific embodiments, let the uncertain input variable The cumulative distribution function of , then the standardization process can be achieved by the following formula:

[0077] In the formula, For about The inverse cumulative distribution function of the standard normal distribution is Standard input variables The standard distribution function of .

[0078] Step 2: Based on the distribution type of the standard input variables, perform polynomial chaos expansion on the output of the distribution network system, perform sparse processing on the basis functions of the polynomial chaos expansion, perform numerical integration on the standard input variables to calculate the polynomial chaos expansion coefficients, and use the obtained polynomial chaos expansion as a high-dimensional proxy model of the distribution network system output.

[0079] As is known, polynomial chaos expansion PCE uses polynomial basis to form random space to describe and propagate the uncertainty of random variables. The essence is to use the excellent performance of orthogonal polynomials to establish a proxy model through the mapping process from random variable input to response. This method has good convergence, is easy to use, and can be well applied to complex systems.

[0080] Orthogonal polynomial basis functions include Hermite polynomials, Legendre polynomials, etc. Each polynomial basis function is suitable for different types of probability distributions. Selecting a suitable basis function is a key step in achieving effective expansion, which usually needs to be determined in combination with the characteristics of random variables.

[0081] In the embodiment of normalizing the distribution form of the uncertain input variable to a normal distribution, a Hermite orthogonal polynomial basis corresponding to the normal distribution is used to perform a polynomial chaos expansion on the output of the distribution network system. The polynomial chaos expansion is:

[0082]

[0083] In the formula, Output of the distribution network system, Input variables for multidimensional criteria, is the number of standard input variables, is the multiple exponent of a term in the polynomial chaos expansion, indicating the power of each standard input variable in the corresponding term, Standard input variables The order of is the set of multiple exponentials of the polynomial, is the polynomial chaos expansion coefficient, For about The polynomial basis function of is expressed as:

[0084]

[0085] In the formula, Standard input variables The order of The basis function of .

[0086] As is known, when facing multi-dimensional random input variables, the full-order polynomial chaos method requires a large number of polynomial terms to maintain the expansion accuracy, which has a high computational cost. Therefore, Sparse Polynomial Chaos Expansion (SPCE) came into being.

[0087] Sparse polynomial chaos expansion (SPCE) is a variant of PCE. Its core idea is to introduce sparsity, which means that only some basis functions will be selected to build the final model during the polynomial expansion process. Sparse polynomial chaos expansion inherits the ability of traditional polynomial chaos expansion to handle uncertainty. By retaining only the polynomial terms that contribute significantly to the output variable, the number of polynomial terms required for calculation is greatly reduced, thereby reducing the computational complexity and maintaining high accuracy. SPCE is particularly critical when dealing with high-dimensional systems, because traditional PCE will cause a sharp increase in computational burden due to combinatorial explosion.

[0088] In some specific embodiments, the method of sparse polynomial basis functions includes: performing hyperbolic truncation processing on the polynomial chaotic expansion output by the distribution network system using a hyperbolic truncation method to obtain a hyperbolic truncation polynomial chaotic expansion.

[0089] Specifically, in the hyperbolic truncation process, we introduce Norm vs. Multiple Exponential To impose constraints:

[0090]

[0091] In the formula, For multiple indexes of norm, where ; The standard input variable The order of As the base number, The norm is the power calculation of the exponent, The preset maximum truncation order.

[0092] is an artificially set hyperparameter used to control the degree of penalty for high-order cross terms. , is the traditional full-order truncation strategy, that is, retaining all , and in this embodiment, , high-order cross terms will be "reduced" or "sparsed", most high-dimensional coupling terms, such as high-order terms containing multiple variables at the same time, will be excluded, retaining low interaction terms and gradually reducing the interaction order of polynomials.

[0093] The entire constraint It means: only retain the multiple exponential combination items that satisfy the norm less than or equal to the preset maximum truncation order, so as to achieve the effect of controlling the computational complexity.

[0094] In some specific embodiments, the standard input variable is a multidimensional standard input variable; accordingly, the numerical integration is a multidimensional numerical integration; then, when calculating the polynomial chaos expansion coefficient by numerically integrating the standard input variable, firstly, a multidimensional integration point is obtained by combining the one-dimensional integration points of each standard input variable; then, numerical integration is performed based on the multidimensional integration points to approximately calculate the polynomial chaos expansion coefficient, and the calculation formula is:

[0095]

[0096] In the formula, is the polynomial chaos expansion coefficient, is the normalization coefficient, is the number of groups of multidimensional integration points, For the Set of multidimensional integration points, For the The weights of the multidimensional integration points, For the The calculation results of the polynomial chaos expansion at the multidimensional integration points of the group, For the Polynomial basis functions at the multidimensional integration points.

[0097] It should be noted that the normalization coefficient in the formula The purpose of is to deal with the case of non-normalized basis functions, that is, if the selected polynomial basis function is only orthogonal but not normalized, then the normalization coefficients Make the polynomial basis functions orthogonal and normalized. If the polynomial basis functions are already orthogonal and normalized, then .

[0098] Generally, if the distribution of the input variable conforms to the common "standard distribution", such as normal distribution, uniform distribution, Beta distribution, etc., the corresponding orthogonal basis functions often have normalized or semi-normalized constants available for reference in the literature. For example, the common Legendre polynomials (uniform distribution) or Hermite polynomials (normal distribution) have known norm coefficients and do not require additional integral calculations.

[0099] In order to significantly reduce the computational complexity, the present invention not only performs sparse processing on the basis functions of the polynomial chaotic expansion, but also optimizes the integral points for the numerical integration of solving the polynomial chaotic expansion coefficients.

[0100] As is known, numerical integration is used to find the approximate value of a definite integral. In mathematical analysis, it is not always possible to calculate the definite integral of a given function. Many definite integrals cannot be accurately calculated using known integral formulas.

[0101] Numerical integration is to use numerical approximation to approximate the given definite integral value. With the help of electronic computing equipment, numerical integration can quickly and efficiently calculate complex integrals. There are many ways to construct numerical integration formulas and integration points, such as Romberg quadrature formula, Newton-Cotes integration formula, Green formula, Gauss integral, Simpson formula and Clenshaw-Curtis integration formula. They all have their own applicable scenarios. It can be seen that the reasonable setting and optimization of integration points have a great influence on the calculation of polynomial chaos expansion coefficients.

[0102] The Clenshaw-Curtis quadrature method is an efficient numerical integration technique.

[0103] In this embodiment, the Clenshaw-Curtis integral formula is used in the interval Internal sampling is performed to obtain the one-dimensional integration points of the standard input variable. Specifically, the midpoint 0 of the interval is taken as the initial point, and integration points are gradually added on both sides of the initial point according to the order of Clenshaw-Curtis integration. The number of integration points is calculated as follows:

[0104]

[0105] In the formula, is the order of the Clenshaw-Curtis integral, is the number of integration points corresponding to the order.

[0106] In some specific embodiments, the one-dimensional integration points of each standard input variable are combined in the following manner: Smolyak sparse grid technology is used to perform linear combination of tensor products on integration points of different dimensions to construct a high-dimensional sparse grid to reduce the number of configuration points.

[0107] The Smolyak sparse grid technology uses one-dimensional integral points of differential combination to construct multi-dimensional integral points in multi-dimensional space, skipping a large number of high-dimensional interaction points. If the Smolyak sparse grid or other optimization strategies are not introduced, the full tensor product will be performed on the one-dimensional integral points of each dimension to obtain multi-dimensional product nodes.

[0108] In 2D For example, if the levels of each dimension can be , the full tensor product takes into account There are 9 combinations in total. If the sum of the pre-set required levels does not exceed 4, it will be skipped. This type of combination is greater than 4, thus reducing many high-order nodes. The level here can be understood as the level of one-dimensional integration accuracy. The higher the level, the more one-dimensional integration points and the higher the accuracy.

[0109] exist In dimensional space, if we use One-dimensional integration points, the total number of integration points for the full tensor product will be ,when When larger, It will explode, forming a "dimensionality disaster" and a heavy computational burden. The Smolyak sparse grid selectively combines the one-dimensional integration points of each dimension, skips a large number of "high-order × high-order" interaction terms, and only retains the parts that contribute significantly to the overall accuracy to reduce the number of multi-dimensional integration points. Therefore, for the same target accuracy requirements, the number of sparse grid points constructed by Smolyak is much lower than the full tensor product, and the numerical results can still achieve approximate accuracy. In other words, under the same accuracy requirements, the number of sparse grid points is often much lower than the full tensor product.

[0110] Step 3: Perform probabilistic power flow calculation on the distribution network system based on the high-dimensional agent model to obtain the statistical characteristics of the output variables of the distribution network system, and perform static risk assessment on the distribution network system based on the statistical characteristics of the output variables of the distribution network system.

[0111] Specifically, static risk assessment includes: node voltage over-limit risk assessment, branch overload risk assessment and system comprehensive risk assessment; the statistical characteristics of the output variables of the distribution network system include: the cumulative distribution function of the node voltage and the cumulative distribution function of the branch transmission power.

[0112] Example 2

[0113] Based on Example 1, this example provides a more comprehensive method for sparsifying polynomial basis functions.

[0114] After numerically integrating the standard input variables to calculate the polynomial chaos expansion coefficients, the Lasso regression algorithm is used to reduce the polynomial chaos expansion coefficients corresponding to some polynomial basis functions to zero, specifically:

[0115] Establish the optimization objective function of Lasso regression:

[0116]

[0117] In the formula, is the polynomial chaos expansion coefficient vector, The corresponding minimization of the objective function , For the The polynomial basis functions at the multidimensional integration points of the group, For the The real output of the distribution network system at the group integration point; is the regularization coefficient, is the absolute value of the polynomial chaos expansion coefficient.

[0118] Specifically, the polynomial chaotic expansion coefficients calculated by numerical integration are used as input, and the Lasso regression algorithm is used to sparse these expansion coefficients by imposing penalties, thereby screening out the basis functions and their coefficients that contribute most significantly to the output, and finding the optimal solution, thereby completing the construction of the overall model and the sparseness of the basis functions.

[0119] In practical applications, a series of candidate regularization coefficients are usually set first The corresponding validation error is calculated by cross-validation method, and finally the polynomial chaos expansion is selected to have good accuracy and maintain good sparsity. value.

[0120] Example 3

[0121] Based on Example 1, this example provides specific content of static risk assessment of the distribution network system.

[0122] First, node voltage over-limit risk assessment includes:

[0123] According to the cumulative distribution function of the node voltage, the probability of each node voltage exceeding the limit is obtained:

[0124]

[0125] In the formula, For Node The voltage amplitude, For Node The upper limit of the voltage amplitude is For Node The lower limit of the voltage amplitude is for Greater than The probability of for Less than The probability of and Node The probability of the voltage exceeding the upper limit and the probability of exceeding the lower limit; for The cumulative distribution function of for The cumulative distribution function of .

[0126] In some specific embodiments, and The values ​​are 0.95pu and 1.05pu respectively.

[0127] In order to flexibly quantify the severity of the voltage over-limit risk, an exponential function is used to quantify the voltage over-limit degree:

[0128]

[0129] In the formula, For about An exponential function of is an exponential function with the natural constant e as base;

[0130] Calculate the risk of node voltage exceeding the limit:

[0131]

[0132] In the formula, For Node The voltage over-limit risk value.

[0133] Secondly, the branch overload probability is obtained according to the cumulative distribution function of branch transmission power:

[0134]

[0135] In the formula, For branch The transmission power, For branch The upper limit power value allowed to be carried, For branch The overload rate, for Greater than The probability of for The cumulative distribution function of

[0136] An exponential function is used to quantify the severity of branch overload:

[0137]

[0138] Calculate the branch overload risk:

[0139]

[0140] In the formula, For about An exponential function of For branch overload risk value.

[0141] In some specific embodiments, the branch The upper limit power value allowed to be carried Take 80% of the rated power value.

[0142] Third, the system comprehensive risk assessment includes:

[0143] The system comprehensive risk index is calculated based on the node voltage over-limit risk and branch overload risk. The calculation formula is:

[0144]

[0145] In the formula, is the first comprehensive risk indicator, is the second comprehensive risk indicator, is the number of nodes in the distribution network system, is the number of branches in the distribution network system; is the first weight coefficient, is the second weight coefficient, .

[0146] It can be seen that using the method of the present invention to perform risk assessment on the distribution network system can not only accurately quantify the probability distribution of node voltage and branch power, but also effectively assess the risk of over-limit and overload, providing a scientific basis for the safety assessment and scheduling decision-making of the distribution network system.

[0147] Example 4

[0148] This example evaluates the applicability and performance of the method of the present invention in a large-scale, high-dimensional distribution network, especially in terms of computational accuracy and efficiency.

[0149] In this embodiment, the standard IEEE-118 node distribution system in the matpower power flow calculation toolbox is selected as the test system, and the analysis and simulation are performed on the MATLAB simulation platform.

[0150] The reference voltage of the test system is 11kV, the reference capacity is 10MVA, and the safety range of the node voltage is set to 0.95~1.05pu. In order to simulate the uncertainty input variables in the system, the load active power fluctuations of 50 nodes are set as random input variables. In addition, wind turbines are connected to nodes 20, 42, 50 and 111, with rated powers of 500kW, 500kW, 600kW and 600kW respectively; photovoltaic battery groups are connected to nodes 37, 74 and 97. Tables 1 and 2 are the relevant parameters of wind turbines and photovoltaic battery groups respectively.

[0151] Table 1: Wind turbine related parameters

[0152]

[0153] Table 2: Parameters of photovoltaic battery pack

[0154]

[0155] In order to verify the accuracy and efficiency advantages of the method of the present invention in probabilistic power flow calculation, The calculation results of the Monte Carlo simulation method based on random sampling are used as a benchmark for evaluating the accuracy and efficiency of the traditional polynomial chaos expansion method and SPCE.

[0156] It should be noted that the traditional polynomial chaos expansion method PCE refers to the process of polynomial chaos expansion without using the hyperbolic truncation strategy (taking ), and the multidimensional integration points are obtained by the full tensor product method.

[0157] This test system analyzes the polynomial expansion with 57 random input variables, including: the load active power of 50 nodes, the output of 4 wind turbines, the output of 3 photovoltaic batteries, and the maximum allowable order. .

[0158] The number of expanded items of PCE is 1711. After the sparse processing proposed by the present invention, taking node 33 as an example, its voltage amplitude is used as the output response of the distribution network system, and its polynomial proxy model only retains 25 basis functions. The proxy model with the active power of branch 10-11 as the output retains 31 basis functions, which significantly reduces the computational complexity.

[0159] Figure 2 The comparison results of the probability density distribution PDF and the cumulative distribution function CDF of the voltage amplitude at node 33 under three methods (PCE, MCS and SPCE) are shown. In the figure, the peak-shaped comparison curve is the probability density distribution PDF, and the continuously increasing comparison curve is the cumulative distribution function CDF.

[0160] from Figure 2 It can be observed that the curve generated by SPCE is almost completely consistent with the MCS reference result, indicating that SPCE can accurately characterize the probabilistic characteristics of branch power. In addition, SPCE is highly consistent with traditional PCE, further verifying the reliability of SPCE in conventional scenarios.

[0161] Figure 2 The refinement of the local magnified area shows that SPCE has excellent fitting ability for the tail region of the probability distribution, which significantly reduces the errors of low-probability events such as extreme power fluctuations. This excellent fitting ability for the tail region of the probability distribution is particularly important because tail events have a significant impact on system risk assessment.

[0162] Figure 3The comparison results of the probability density distribution PDF and the cumulative distribution function CDF of the active power of branch 10-11 under three methods (PCE, MCS and SPCE) are shown. In the figure, the peak-shaped comparison curve is the probability density distribution PDF, and the continuously increasing comparison curve is the cumulative distribution function CDF.

[0163] from Figure 2 It can be observed that both SPCE and PCE are highly consistent with MCS in the entire cumulative probability distribution range. However, the local magnification area shows that SPCE has a more accurate description ability in the small probability range, which gives it a clear advantage in risk assessment applications.

[0164] Table 3: Comparison of calculation accuracy and efficiency of voltage amplitude at node 33 in IEEE-118 node system

[0165]

[0166] Table 3 shows the comparison results of computation time and error indicators. SPCE takes 65.10s while maintaining high accuracy, which is only 4.87% of PCE. Compared with the benchmark MCS of 4476.35s, the computational efficiency is improved by two orders of magnitude. This result verifies that SPCE can not only maintain high-precision computation results when processing complex high-dimensional systems, but also significantly improve computational efficiency.

[0167] Table 4: Comparison of risk assessment results of different methods for IEEE-118 node system

[0168]

[0169] Table 4 shows the ranking of risk assessment results based on SPCE, MCS and two-point estimation (TPE) in the IEEE-118 node test system. It can be seen that the rankings of SPCE and MCS are basically consistent, which further verifies the reliability of the proposed method in risk assessment of complex and high-dimensional distribution networks.

[0170] Example 5

[0171] This embodiment provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the static risk assessment method for a distribution network system described in any one of Embodiments 1-3.

[0172] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A static risk assessment method for a distribution network system, characterized in that: include: Standardize the uncertain input variables in the distribution network system to obtain standard input variables that obey the preset probability distribution; Based on the distribution type of the standard input variables, a polynomial chaos expansion is performed on the output of the distribution network system, a basis function of the polynomial chaos expansion is sparsely processed, the standard input variables are numerically integrated to calculate the polynomial chaos expansion coefficients, and the obtained polynomial chaos expansion is used as a high-dimensional proxy model of the output of the distribution network system; Based on the high-dimensional agent model, a probabilistic power flow calculation is performed on the distribution network system to obtain statistical characteristics of output variables of the distribution network system; Based on the statistical characteristics of the output variables of the distribution network system, a static risk assessment is performed on the distribution network system.

2. The static risk assessment method for distribution network system according to claim 1, characterized in that: The default probability distribution is the standard normal distribution; the formula for standardizing the uncertain input variables in the distribution network system is: , in, Enter variables for uncertainty The cumulative distribution function of For about The inverse cumulative distribution function of the standard normal distribution is Standard input variables The standard distribution function of .

3. The method for static risk assessment of distribution network system according to claim 1, characterized in that: The sparse processing of the basis functions of the polynomial chaos expansion comprises: The polynomial chaos expansion of the distribution network system output is: In the formula, Output of the distribution network system, Input variables for multidimensional criteria, is the number of standard input variables, is a multiple index, is the set of multiple exponentials of the polynomial, is the polynomial chaos expansion coefficient, For about The polynomial basis function of is expressed as: ， In the formula, Standard input variables The order of Standard input variables The order of The basis functions of The hyperbolic truncation method is used to perform hyperbolic truncation on the polynomial chaotic expansion output by the distribution network system to obtain the hyperbolic truncation polynomial chaotic expansion, which is specifically: In the hyperbolic truncation process, we introduce Norm vs. Multiple Exponential Imposing restrictions: In the formula, For multiple indexes of norm, where ; The standard input variable The order of As the base number, The norm is the power calculation of the exponent, is the preset highest truncation order.

4. The method for static risk assessment of a distribution network system according to claim 1, characterized in that: The standard input variable is a multidimensional standard input variable; The numerical integration is a multi-dimensional numerical integration; The method of performing numerical integration on the standard input variables to calculate the polynomial chaos expansion coefficients includes: Get multi-dimensional integral points; Based on the multi-dimensional integration points, numerical integration is performed to approximately calculate the polynomial chaos expansion coefficients, and the calculation formula is: In the formula, is the polynomial chaos expansion coefficient, is the normalization coefficient, is the number of groups of multidimensional integration points, For the Set of multidimensional integration points, For the The weights of the multidimensional integration points, For the The calculation results of the polynomial chaos expansion at the multidimensional integration points of the group, For the Polynomial basis functions at the multidimensional integration points.

5. The method for static risk assessment of distribution network system according to claim 4, characterized in that: The multi-dimensional integration points are obtained by combining the one-dimensional integration points of each standard input variable; The one-dimensional integration points of the standard input variables are obtained by the Clenshaw-Curtis integration formula, specifically: In the interval In the interval, the midpoint 0 is taken as the initial point, and integration points are gradually added on both sides of the initial point according to the order of Clenshaw-Curtis integration. The number of integration points is calculated as follows: In the formula, is the order of the Clenshaw-Curtis integral, is the number of integration points corresponding to the order.

6. The method for static risk assessment of a distribution network system according to claim 5, characterized in that: The one-dimensional integration points of each standard input variable are combined in the following way: the Smolyak sparse grid technique is used to perform linear combinations of tensor products on integration points of different dimensions to construct a high-dimensional sparse grid.

7. The method for static risk assessment of a distribution network system according to claim 1, characterized in that: After the standard input variables are numerically integrated to calculate the polynomial chaos expansion coefficients, the method further includes: using a Lasso regression algorithm to reduce the polynomial chaos expansion coefficients corresponding to some polynomial basis functions to zero, specifically: Establish the optimization objective function of Lasso regression: In the formula, is the polynomial chaos expansion coefficient vector, The corresponding minimization of the objective function , is the number of groups of multidimensional integration points, For the The polynomial basis functions at the multidimensional integration points of the group, For the The actual output of the distribution network system at the group integration point, is a multiple index, is the set of multiple exponentials of the polynomial, is the absolute value of the polynomial chaos expansion coefficient, is the regularization coefficient; Using the cross-validation method, Select the best performing candidate from the candidate set value.

8. The method for static risk assessment of a distribution network system according to claim 1, characterized in that: Based on the statistical characteristics of the output variables of the distribution network system, a static risk assessment is performed on the distribution network system, including: Based on the statistical characteristics of the output variables of the distribution network system, a cumulative distribution function of the node voltage and a cumulative distribution function of the branch transmission power are obtained; The probability of each node voltage exceeding the limit is obtained according to the cumulative distribution function of the node voltage: In the formula, For Node The voltage amplitude, For Node The upper limit of the voltage amplitude is For Node The lower limit of the voltage amplitude is for Greater than The probability of for Less than probability; and Node The probability of the voltage exceeding the upper limit and the probability of exceeding the lower limit; for The cumulative distribution function of for The cumulative distribution function of An exponential function is used to quantify the voltage limit: In the formula, For about An exponential function of is an exponential function with the natural constant e as base; Calculate the risk of node voltage exceeding the limit: In the formula, For Node The voltage over-limit risk value; The branch overload probability is obtained according to the cumulative distribution function of the branch transmission power: In the formula, For branch The transmission power, For branch The upper limit power value allowed to be carried, For branch The overload probability, for Greater than probability; for The cumulative distribution function of An exponential function is used to quantify the severity of branch overload: Calculate the branch overload risk: In the formula, For about An exponential function of For branch overload risk value.

9. The method for static risk assessment of a distribution network system according to claim 8, characterized in that: The static risk also includes: calculating the comprehensive risk index of the distribution network system, the calculation formula is: In the formula, is the first comprehensive risk indicator, is the second comprehensive risk indicator, is the number of nodes in the distribution network system, is the number of branches in the distribution network system; is the first weight coefficient, is the second weight coefficient, .

10. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the static risk assessment method for a distribution network system according to any one of claims 1 to 9.

Images