A static risk assessment method and device for distribution network system

Abstract

The present invention relates to a method and device for static risk assessment of a distribution network system, and belongs to the technical field of power systems. The method comprises: standardizing the uncertain input variables in the distribution network system to obtain standard input variables; performing polynomial chaos expansion on the output of the distribution network system, performing sparse processing on the basis functions of the polynomial chaos expansion, performing numerical integration on the standard input variables to calculate the polynomial chaos expansion coefficients, and using the obtained polynomial chaos expansion as a high-dimensional proxy model of the output of the distribution network system; and performing static risk assessment on the distribution network system based on the high-dimensional proxy model. The present invention significantly improves the overall computing efficiency under the same accuracy requirements by performing sparse processing on the polynomial basis functions, controlling the basis function dimensions, and then calculating the polynomial coefficients by numerical integration, thereby meeting the demand for real-time assessment of the static risks of the new intelligent distribution network system.

Description

Technical Field

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

[0002] With the rapid growth of renewable energy generation and the widespread access to distributed resources, the operational model of distribution networks is undergoing profound changes. However, the intermittent and random nature of renewable energy sources such as wind and photovoltaic power, coupled with the dynamic fluctuations in load demand, pose significant operational risks and stability challenges to distribution networks under high penetration conditions. This increase in uncertainty makes it difficult for traditional deterministic analysis methods to fully reflect the complexity of system operation. Efficient and accurate risk assessment technologies are urgently needed to provide a scientific basis for optimizing the dispatch and ensuring the safety of distribution networks.

[0003] Existing risk assessment methods are primarily categorized as deterministic and probabilistic. Deterministic assessment methods tend to be conservative due to their assumptions of extreme conditions and their neglect of the probabilistic nature of operating states. Probabilistic risk assessment methods, through probabilistic power flow analysis, can provide a more comprehensive description of system states. However, traditional probabilistic methods, such as Monte Carlo simulation (MCS), are computationally expensive and struggle to meet real-time requirements. Although subsequent techniques such as variance reduction and approximate expansion have been proposed, the full tensor product leads to an exponential growth in the number of configuration points when the dimensions are large, creating a "curse of dimensionality" in high-dimensional scenarios. Furthermore, traditional polynomial chaos expansion (PCE) methods often face the dilemma of a simultaneous surge in the number of basis functions and integration points in high-dimensional random variables, significantly reducing overall computational efficiency. Therefore, balancing accuracy and efficiency has become a core issue that needs to be 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 distribution network systems, which solves the problem faced by traditional PCE in the case of high-dimensional random variables where the number of basis functions and the number of integration points increase simultaneously.

[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 subjected to sparse processing, 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 distribution network system output;

[0009] Performing probabilistic power flow calculation on the distribution network system based on the high-dimensional agent model 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 default probability distribution is the standard normal distribution; the formula for standardizing the uncertainty 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] Where, is the output of the distribution network system, For multidimensional standard input variables, 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] Where, Standard input variables The order of Standard input variables The order of 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 versus multiple exponential Imposing restrictions:

[0021]

[0022] Where, For multiple indexes of norm, where ; The standard input variable The order of As the base, 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; and 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 coefficient, and the calculation formula is:

[0026]

[0027] Where, is the polynomial chaos expansion coefficient, is the normalization coefficient, is the number of groups of multidimensional integration points, For the Group multidimensional integration points, For the The weights of the group 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 set of 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] Where, is the order of the Clenshaw-Curtis integral, 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 way: the Smolyak sparse grid technique is used to perform linear combination of tensor products on the 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] Where, is the polynomial chaos expansion coefficient vector, To minimize the objective function , is the number of groups of multidimensional integration points, For the polynomial basis functions at the set of multidimensional integration points, For the The actual 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, the 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 of the distribution network system is performed, including:

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

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

[0041]

[0042] Where, For nodes The voltage amplitude, For nodes The upper limit of the voltage amplitude, For nodes The lower limit of the voltage amplitude, 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

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

[0044]

[0045] Where, For about The exponential function of is an exponential function with the natural constant e as the base;

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

[0047]

[0048] Where, For nodes 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] Where, 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

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

[0053]

[0054] Calculate branch circuit overload risk:

[0055]

[0056] Where, For about The exponential function of For branch overload risk value.

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

[0058]

[0059] Where, 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 of the 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 retaining the multi-exponential combination terms that satisfy the norm less than or equal to the preset maximum truncation order, 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 distribution network system provided by the present invention adopts Smolyak sparse grid technology to replace the traditional full tensor product. By differentially combining one-dimensional integration points in multidimensional space, most of the "high-order × high-order" interaction terms are skipped, which greatly reduces the number of multidimensional integration points and the computational burden, effectively solving the problem of explosive growth of 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 chaos expansion coefficient to sparse the expansion coefficient and obtain the optimal solution, thereby further achieving effective simplification of the basis function and improving the computational efficiency;

[0066] (5) The static risk assessment method of 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 over-limit risk and overload risk, providing a scientific basis for the safety assessment and scheduling decision-making of the new distribution network system. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0068] Figure 2 1 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 This 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 are 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 embodiments described are only some embodiments of the present application, not all embodiments.

[0071] Currently, smart distribution grid systems, characterized by the integration of distributed wind and solar power generation and the integration of new re-electrified loads, have become a crucial link between green energy production and low-carbon consumption. However, the intermittent nature of high-proportion renewable energy generation and the stochastic nature of large-scale heterogeneous loads (such as electric vehicles and air conditioners) significantly impact the operation of distribution networks. Therefore, it is necessary to analyze the propagation of source-load uncertainty, develop methods to quantify operational uncertainty in distribution networks, and implement static risk assessments to ensure the safe and economic operation of smart distribution grids.

[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: renewable 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 distributions and map them to a standard distribution.

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

[0077] Where, 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 distribution network system output, 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] The well-known Polynomial Chaos Expansion (PCE) uses a polynomial basis to construct a random space to describe and propagate the uncertainty of random variables. Essentially, it leverages the superior properties of orthogonal polynomials to establish a surrogate model by mapping random variable inputs to responses. This method exhibits good convergence, is easy to use, and is well-suited for complex systems.

[0080] Orthogonal polynomial basis functions include Hermite polynomials and Legendre polynomials. Each polynomial basis function is suitable for different probability distributions. Choosing the right basis function is a key step in achieving an effective expansion, and this is usually determined by considering the characteristics of the random variable.

[0081] In an embodiment in which the distribution form of the uncertain input variable is standardized 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] Where, is the output of the distribution network system, For multidimensional standard input variables, 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] Where, Standard input variables The order of The basis functions of .

[0086] It is well known that full-order polynomial chaos methods are computationally expensive when dealing with multidimensional random input variables, as they require a large number of polynomial terms to maintain the accuracy of the expansion. Therefore, sparse polynomial chaos expansion (SPCE) has emerged.

[0087] Sparse Polynomial Chaotic Expansion (SPCE) is a variant of PCE. Its core concept is to introduce sparsity. Sparsity means that during the polynomial expansion process, only a subset of basis functions are selected to construct the final model. While inheriting the traditional polynomial chaotic expansion's ability to handle uncertainty, sparse polynomial chaotic expansion significantly reduces the number of polynomial terms required by retaining only those that significantly contribute to the output variable, thereby lowering computational complexity while maintaining high accuracy. SPCE is particularly critical when dealing with high-dimensional systems, as traditional PCE can lead to a dramatic increase in computational burden due to combinatorial explosion.

[0088] In some specific embodiments, the method of sparsifying the polynomial basis function 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 versus multiple exponential To impose constraints:

[0090]

[0091] Where, For multiple indexes of norm, where ; The standard input variable The order of As the base, 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, which is to keep 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 the polynomials.

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

[0094] In some specific embodiments, the standard input variables are multidimensional standard input variables; accordingly, the numerical integration is a multidimensional numerical integration; then, when calculating the polynomial chaos expansion coefficient by numerically integrating the standard input variables, first, multidimensional integration points are 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] Where, is the polynomial chaos expansion coefficient, is the normalization coefficient, is the number of groups of multidimensional integration points, For the Group multidimensional integration points, For the The weights of the group 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 set of 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 functions are 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 input variable distribution conforms to a common "standard distribution," such as normal, uniform, or Beta, the corresponding orthogonal basis functions often have normalized or semi-normalized constants readily available in the literature. For example, the norm coefficients of the common Legendre polynomials (uniform distribution) or Hermite polynomials (normal distribution) are known constants, eliminating the need for additional integration.

[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 integration points of the numerical integration for solving the polynomial chaotic expansion coefficients.

[0100] As is well known, numerical integration is used to approximate the 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 uses numerical approximation to approximate the value of a given definite integral. With the help of electronic computing equipment, numerical integration can quickly and efficiently calculate complex integrals. Numerous methods exist for constructing numerical integration formulas and integration points, such as the Romberg quadrature formula, the Newton-Cotes integral formula, Green's formula, Gauss's integral, the Simpson formula, and the Clenshaw-Curtis integral formula. Each of these methods has its own application scenarios, demonstrating that the proper setting and optimization of integration points significantly impacts the calculation of polynomial chaotic 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 used as the initial point, and integration points are gradually added on both sides of the initial point according to the order of the Clenshaw-Curtis integral. The number of integration points is calculated as follows:

[0104]

[0105] Where, 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 by performing a linear combination of tensor products on integration points of different dimensions using the Smolyak sparse grid technique to construct a high-dimensional sparse grid to reduce the number of configuration points.

[0107] The Smolyak sparse grid technology uses one-dimensional integration points of differential combination to construct multidimensional integration points in multidimensional 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 integration points of each dimension to obtain multidimensional 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 pre-set required level and the sum does not exceed 4, it will be skipped. This type of combination has a sum 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 it is larger, The number of multidimensional integration points will explode, forming a "curse of dimensionality" and imposing an extremely heavy computational burden. However, using a Smolyak sparse grid selectively combines one-dimensional integration points in each dimension, skipping numerous "high-order × high-order" interaction terms and retaining only those that significantly contribute to overall accuracy, thereby reducing the number of multidimensional integration points. Therefore, for the same target accuracy, the number of points in the sparse grid constructed by Smolyak is far lower than that of the full tensor product, while the numerical results still achieve similar accuracy. In other words, under the same accuracy requirement, the number of points in a sparse grid is often far lower than that of 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 distribution network system output variables include: the cumulative distribution function of node voltage and the cumulative distribution function of 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] Where, is the polynomial chaos expansion coefficient vector, The corresponding minimization of the objective function , For the polynomial basis functions at the set of multidimensional integration points, For the The actual 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 chaos expansion coefficients calculated by numerical integration are used as input. The Lasso regression algorithm applies a penalty to these expansion coefficients to achieve sparsification, screening out the basis functions and their coefficients that contribute most significantly to the output. The optimal solution is then found, completing the overall model construction and basis function sparsification.

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

[0124]

[0125] Where, For nodes The voltage amplitude, For nodes The upper limit of the voltage amplitude, For nodes The lower limit of the voltage amplitude, 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 .

[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] Where, For about The exponential function of is an exponential function with the natural constant e as the base;

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

[0131]

[0132] Where, For nodes The voltage over-limit risk value.

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

[0134]

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

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

[0137]

[0138] Calculate branch circuit overload risk:

[0139]

[0140] Where, For about The 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, comprehensive system 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] Where, 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 over-limit risk and overload risk, 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] This embodiment selects the standard IEEE-118 node power distribution system in the matpower power flow calculation toolbox as the test system, and performs analysis and simulation on the MATLAB simulation platform.

[0150] The test system's reference voltage is 11 kV, its reference capacity is 10 MVA, and the node voltage safety range is set to 0.95–1.05 pu. To simulate the uncertain input variables in the system, the load active power fluctuations at 50 nodes are set as random input variables. Furthermore, wind turbines are connected to nodes 20, 42, 50, and 111, with rated powers of 500 kW, 500 kW, 600 kW, and 600 kW, respectively. Photovoltaic arrays are connected to nodes 37, 74, and 97. Tables 1 and 2 list the relevant parameters for the wind turbines and photovoltaic arrays, respectively.

[0151] Table 1: Wind turbine parameters

[0152]

[0153] Table 2: Parameters of photovoltaic cell arrays

[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 random sampling-based Monte Carlo simulation method are used as a benchmark to evaluate 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, and the output of 3 photovoltaic cells. .

[0158] The number of expanded terms in the PCE is 1711. However, after the sparsification process proposed in this invention, taking node 33 as an example, where its voltage amplitude is used as the distribution network system output response, its polynomial proxy model retains only 25 basis functions. The proxy model using the active power of branch 10-11 as the output retains 31 basis functions, significantly reducing computational complexity.

[0159] Figure 2 The figure shows the comparison results of the probability density distribution PDF and cumulative distribution function CDF of the voltage amplitude at node 33 under three methods (PCE, MCS, and SPCE). 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 The curves generated by SPCE are almost identical to the MCS reference results, demonstrating that SPCE can accurately characterize the probabilistic characteristics of branch power. Furthermore, SPCE maintains high consistency with traditional PCE, further validating its reliability in common scenarios.

[0161] Figure 2 The refinement of the local magnified area shows that SPCE has an excellent fitting ability for the tail region of the probability distribution, which significantly reduces the error 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 figure shows the comparison results of the probability density distribution (PDF) and cumulative distribution function (CDF) of the active power of branch 10-11 under three methods (PCE, MCS, and SPCE). 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 across the entire cumulative probability distribution. However, a zoomed-in view of the local area shows that SPCE has a more accurate description capability within 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 bus system

[0165]

[0166] Table 3 shows a comparison of computation time and error metrics. While maintaining high accuracy, SPCE takes only 65.10 seconds, only 4.87% of PCE. Compared to the benchmark MCS's 4476.35 seconds, this represents a two-order-of-magnitude improvement in computational efficiency. This result demonstrates that SPCE can not only maintain high-precision computational results but also significantly improve computational efficiency when dealing with complex, high-dimensional systems.

[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, further verifying the reliability of the proposed method in risk assessment of complex, 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 subjected to sparse processing, 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 distribution network system output; Performing probabilistic power flow calculation on the distribution network system based on the high-dimensional agent model to obtain statistical characteristics of output variables of the distribution network system; Performing a static risk assessment on the distribution network system based on the statistical characteristics of the output variables of the distribution network system; The step of performing sparse processing on the basis functions of the polynomial chaotic expansion includes: The polynomial chaos expansion of the distribution network system output is: Where Y is the output of the distribution network system, X=[x1,x2,…,x M ] is a multidimensional standard input variable, M is the number of standard input variables, α is the multi-index, A is the multi-index set of the polynomial, y α is the polynomial chaos expansion coefficient, Ψ α (X) is the polynomial basis function about X, and the expression is: Where, α i The standard input variable x i The order of The standard input variable x i The order is α i 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, the q-norm is introduced to impose restrictions on the multi-exponential α: Where, ‖α‖ q is the q-norm of the multi-index α, where q∈(0,1); The standard input variable x i The order α i is the base, the power is calculated with the q norm as the exponent, and p is the preset highest truncation order; 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: Establish the optimization objective function of Lasso regression: Where y is the polynomial chaos expansion coefficient vector, is the y corresponding to minimizing the objective function, N is the number of multidimensional integration points, Ψ α (x (n) ) is the polynomial basis function at the nth group of multidimensional integration points, Y (n) is the actual output of the distribution network system at the nth set of integration points, α is the multi-index, A is the multi-index set of the polynomial, |y α | is the absolute value of the polynomial chaos expansion coefficient, λ is the regularization coefficient; The cross-validation method is used to select the best performing λ value from the preset λ candidate set.

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 uncertainty input variables in the distribution network system is: Z(x i )=Φ -1 (F(x i ′)) Among them, F(x i ′) is the uncertainty input variable x i The cumulative distribution function of ′, Φ -1 (F(x i ′)) is about F(x i ′), the inverse cumulative distribution function of the standard normal distribution, Z(x i ) is the standard input variable x i The standard distribution function of .

3. The static risk assessment method for 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 coefficient, and the calculation formula is: Where y α is the polynomial chaos expansion coefficient, γ α is the normalization coefficient, N is the number of multidimensional integration points, ξ n is the nth group of multidimensional integration points, w n is the weight of the nth group of multidimensional integration points, is the calculation result of the polynomial chaos expansion at the nth group of multidimensional integration points, Ψ α (ξ n ) is the polynomial basis function at the nth group of multidimensional integration points.

4. The static risk assessment method for distribution network system according to claim 3, 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 variable are obtained by the Clenshaw-Curtis integration formula. Specifically, in the interval [-1, 1], 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 the Clenshaw-Curtis integration. The number of integration points is calculated as follows: Where lcc is the order of the Clenshaw-Curtis integration, and occ(lcc) is the number of integration points corresponding to the order.

5. The static risk assessment method for distribution network system according to claim 4, 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 combination of tensor products on the integration points of different dimensions to construct a high-dimensional sparse grid.

6. 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: obtaining a cumulative distribution function of node voltage and a cumulative distribution function of branch transmission power based on the statistical characteristics of the output variables of the distribution network system; The probability of each node voltage exceeding the limit is obtained according to the cumulative distribution function of the node voltage: P V ( V k )=P(V k <V kmin )=F k (V kmin ) Where V k is the voltage amplitude of node k, V kmax is the upper limit of the voltage amplitude at node k, V kmin is the lower limit of the voltage amplitude at node k, P(V k >V kmax ) is V k Greater than V kmax The probability of P(V k <V kmin ) is V k Less than V kmin probability; and P V ( V k ) are the probability of the voltage at node k exceeding the upper limit and the probability of exceeding the lower limit respectively; F k (V kmax ) is V kmax The cumulative distribution function of k (V kmin ) is V kmin The cumulative distribution function of An exponential function is used to quantify the voltage limit: Where, Sev(V k ) is about V k The exponential function of exp is the exponential function with the natural constant e as the base; Calculate the risk of node voltage exceeding the limit: Where, is the voltage over-limit risk value of node k; The branch overload probability is obtained according to the cumulative distribution function of the branch transmission power: P S (S l )=P(S l >S lmax )=1-F l (S lmax ) Where S l is the transmission power of branch l, S lmax is the upper limit power value allowed to be carried by branch l, P S (S l ) is the overload probability of branch l, P(S l >S lmax ) is S l Greater than S lmax The probability of F l (S lmax ) is S lmax The cumulative distribution function of An exponential function is used to quantify the severity of branch overload: Calculate branch circuit overload risk: Where, Sev(S l ) is about S l The exponential function of is the overload risk value of branch l.

7. The static risk assessment method for distribution network system according to claim 6, characterized in that: The static risk also includes: calculating the comprehensive risk index of the distribution network system, the calculation formula is: Where R OV is the first comprehensive risk indicator, R OL is the second comprehensive risk indicator, N B is the number of nodes in the distribution network system, N L is the number of branches in the distribution network system; β1 is the first weight coefficient, β2 is the second weight coefficient, β1+β2=1.

8. 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 7.

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