A stochastic power flow calculation method based on multiple buds and multidimensional regular embeddings.

Abstract

This provides a stochastic power flow calculation method based on multiple bud solutions and multidimensional regular embeddings. [Solution] The method includes the steps of: sequentially solving quadratic semianalytic solutions of node voltages in sub-intervals of each segment based on a multidimensional regular embedding method for self-adaptive multiple sprout solutions; generating K sample groups based on the probability distribution of random input variables, converting the sample data into embedding variable values, and classifying and reducing them; substituting the embedding variable values ​​into the quadratic semianalytic solutions of node voltages in each sub-interval, calculating Padé approximations in combination with a parallel multivariate quotient method to obtain power flow solutions for each sample; statistically analyzing the power flow solutions for each sample; calculating the expected value and standard deviation of each quantity to be solved; and plotting probability density curves and cumulative distribution curves; and processing uncertainties within the power grid based on the probability density curves and cumulative distribution curves, analyzing and predicting the operational status of the power grid, and identifying potential weaknesses in the power grid.

Description

[Technical Field]

[0001] The present invention relates to the field of power systems, and more particularly to a stochastic power flow calculation method based on multiple sprout-multidimensional regular embedding. [Background technology]

[0002] Stochastic power flow is a crucial foundation for resolving uncertainties within power grids. With the introduction of dual carbon targets, the penetration rate of new energy sources in power grids is continuously increasing (Non-Patent Literature 1). However, wind power output is almost random, and the introduction of large-scale wind power generation can introduce significant uncertainty into the overall system (Non-Patent Literature 2). For this reason, research on stochastic power flow calculations in power grids has become urgently needed.

[0003] Currently, the probabilistic power flow calculation methods commonly used in power systems (Non-Patent Literature 3) include simulation methods, approximation methods, and analysis methods. The simulation method establishes a probabilistic model with uncertain factors as random variables, performs deterministic power flow calculations by repeatedly sampling, and statistically determines the distribution characteristics of the output variables based on the calculation results. The main method is the Monte-Carlo Simulation (MCS) method (Non-Patent Literature 4), but it requires generating a Jacobian matrix for each sample and iteratively solving the energy flow, which takes a long time to compute. The approximation method approximates the statistical characteristics of the output variables using the numerical characteristics of the input random variables, with the main method being the point estimation method (Non-Patent Literature 5). This method is computationally efficient, but the estimation accuracy of the higher-order moments of the random variables is insufficient, and it is not possible to accurately obtain the probability distribution function of the output random variables. The analysis method uses a linearized model of the energy flow equation at the operational point, performs convolution calculations using the relationships between random input variables, and determines the probability distribution of the output variables. The main method is the semi-invariant method (Non-Patent Literature 6). This method is highly computationally efficient, but it produces large errors for highly variable random input variables. All of the above methods involve solving deterministic currents in the computation process, and generally numerical iterative methods such as the Newton-Raphson method (NR) are used. However, the NR method is sensitive to initial values, and if the initial values ​​are not chosen appropriately, the computation time can be long and convergence may not occur. Also, in the computation process of the Newton-Raphson method, the Jacobian matrix is ​​prone to singularities (Non-Patent Literature 7).

[0004] To solve the drawbacks of the NR method in energy flow calculations, Non-Patent Document 8 proposed the Holomorphic Embedding Method (HEM), which uses recursive thinking based on complex analysis theory to solve non-linear equation systems. Compared with the NR method, this method does not require an initial value and does not form a Jacobian matrix. Based on the HEM theory, Non-Patent Document 9 constructed a HEM model for PV nodes and proposed a complete Holomorphic Embedding Load Flow Method (HELM). The above methods enable accurate solution of system power flows but are not associated with the physical meaning of actual system power flows. In Non-Patent Document 10, based on the conventional HELM, further inference was made, and a new concept of physical germ solution was proposed. When solving the power flow of the power system, physical meaning was given to the embedding variables, and it developed into the Multi-Dimensional Holomorphic Embedding Method (MDHEM) with multiple embedding variables. This method can derive the power series formula for the embedding variables with physical meaning offline, which is also called a semi-analytical solution (Non-Patent Document 11). By simply adjusting the embedding variables, power flow calculations for different load scenarios can be quickly realized. Existing MDHEM can avoid the problem that conventional iterative methods need to repeatedly perform steady-state energy flow calculations when solving multiple scenarios, but the semi-analytical solution still requires the coefficients of high-order power series, resulting in a huge amount of calculation.

[0005] How to quickly and accurately realize probabilistic power flow calculation in the power system is an important issue in current research.

Prior Art Documents

Non-Patent Documents

[0006]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

Non-Patent Document 5

Non-Patent Document 6

Non-Patent Document 7

Non-Patent Document 8

Non-Patent Document 9

[0007] This invention provides a method for calculating the stochastic power flow of a power system based on Multi-Germ Solution and Multi-Dimensional Holomorphic Embedding Method (MG-MDHEM), and guarantees the accuracy of the stochastic power flow calculation results. This invention is not only fast but also highly robust, and can be applied to some power systems that cannot be converged by conventional methods. Compared to conventional MCS method stochastic power flow algorithms based on MDHEM, this invention offers clear advantages and enables rapid solving of the stochastic power flow of a power system as follows. [Means for solving the problem]

[0008] A method for calculating power flow based on multiple buds and multidimensional regular embeddings, Based on a multidimensional regular embedding method for self-adaptive multiple sprouts, the variation range of selected random input variables is segmented to set up multiple sprouts, and the quadratic semianalytic solutions of the node voltages in the sub-intervals of each segment are sequentially solved. The process involves generating K sample groups based on the probability distribution of random input variables, converting the sample data into embedding variable values, and then performing classification and reduction. The steps include substituting the embedding variable values ​​into the quadratic semianalytic solution of the node voltage in each sub-interval, calculating the Padé approximation in combination with the parallel multivariate quotient method, obtaining the tidal flow solution for each sample, statistically analyzing the tidal flow solution for each sample, calculating the expected value and standard deviation of each solvable quantity, and plotting the probability density curve and cumulative distribution curve, The process involves processing uncertainties within the power grid based on probability density curves and cumulative distribution curves, analyzing and predicting the operational status of the power grid, and identifying potential weaknesses in the power grid. A calculation method characterized by including the following.

[0009] The sequential calculation of the quadratic semianalytic solutions for the node voltages in the sub-sections of each segment is as follows: By adaptively searching for the convergence interval of the quadratic semianalytic solution of the solvable quantity in the ground state, the segment length of the variation range of the selected random input variable is calculated. After segmentation, the midpoint of each sub-interval is set as the initial point, and the solution at the initial point is found, thereby realizing self-adaptive calculation of multiple bud solutions.

[0010] Searching for the convergence interval of the quadratic semianalytic solution of the solvable quantity in the ground state involves updating the embedding variable values ​​using a variable step size method based on exponential scaling, and the formula is as follows:

[0011]

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[0012]

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[0013]

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[0014] Substituting the embedded variable values ​​into the quadratic semianalytic solution of the node voltage in each sub-interval and calculating the Padé approximation in combination with the parallel multivariate quotient method is specifically as follows: Random variables are converted to embedding variable values, assigned to their respective segment intervals, and substituted into the quadratic semianalytic solutions of the solvable quantities for each segmented sub-interval after reduction. Then, the steady-state flow is calculated K times using the parallel multivariate quotient method.

[0015]

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[0016]

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[0017] The parallel calculation formula of the multivariable quotient difference method is as follows.

[0018]

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Advantages of the Invention

[0019] As the advantageous effects of the technical means provided by the present invention, 1. The present invention can achieve accurate solution of the probabilistic power flow of the power system. Compared with the MCS probabilistic power flow calculation results based on the conventional NR method, the relative error between the two is extremely small. 2. The present invention proposes a self-adaptive multiple sprout MG-MDHEM, which utilizes the characteristic that physical sprouts can be flexibly set to set multiple initial points within the range of variation of random input variables, uses the solution at the initial point as the physical sprout, and sets the semi-analytical solution derived from each physical sprout to a low order in order to suppress computational cost, thereby effectively improving the efficiency of solving the semi-analytical solution and significantly improving the computation speed of the Padé approximation, thereby effectively improving the efficiency of stochastic power flow calculation. 3. The present invention proposes a parallel multivariate quotient method that vectorizes the difference quotient matrix of existing multivariate quotient methods, uses high-dimensional matrix operations instead of numerical calculations, and can synchronously calculate multiple sample currents in combination with the MCS method, resulting in faster computation speed and higher computational efficiency compared to the serial multivariate quotient method. 4. The present invention combines the proposed multiple bud-multidimensional regular embedding method and parallel multivariate quotient method with the MCS method to calculate the stochastic power flow of a power system. Compared to the existing MCS method based on the Newton-Raphson method, the calculation accuracy is almost the same, but the calculation time is shorter, the adaptability is better, and it provides a promising direction for the rapid solution of the stochastic power flow of a power system. The stochastic power flow calculation can handle uncertainties in the power system, such as load fluctuations and uncertainties in new energy output, and can analyze and predict the operating status of the power system, more accurately reflect the actual state of the power system, evaluate the performance of the system under different operating conditions, and also contribute to identifying potential weaknesses in the power grid. [Brief explanation of the drawing]

[0020] [Figure 1] This is a flowchart of the MG-MDHEM stochastic power flow algorithm based on self-adaptive multiple bud solutions. [Figure 2] This is a diagram of the revised IEEE14 test system configuration. [Figure 3] These are the probability distribution curves for V4 and P4-5. [Figure 4] This is a schematic diagram showing the load fluctuation range segments and multiple bud configurations for the modified IEEE14 system. [Figure 5]This is a diagram illustrating the configuration of the MG-MDHEM stochastic power flow calculation system based on self-adaptive multiple bud solutions. [Modes for carrying out the invention]

[0021] Hereinafter, embodiments of the present invention will be described in more detail to further clarify the object, technical means, and advantages of the present invention.

[0022] (Example 1) To achieve rapid and accurate solving of the stochastic power flow of a power system, an embodiment of the present invention provides an MG-MDHEM stochastic power flow calculation method based on a self-adaptive multiple spore solution, the method comprising the following steps: 101: Based on MG-MDHEM of self-adaptive multiple sprouts, the range of variation of selected random input variables is segmented to set up multiple sprouts, and the quadratic semianalytic solutions of the node voltages in the sub-intervals of each segment are sequentially solved. 102: A step to generate K sample groups based on the probability distribution of random input variables, convert the sample data into embedding variable values, and perform classification and reduction. 103: Substitute the embedded variable values ​​into the quadratic semianalytic solution of the node voltage in each sub-interval of step 101, calculate the Padé approximation in combination with the parallel multivariate quotient method, and obtain the tidal flow solution for each sample. 104: Steps to statistically analyze the tidal solutions for each sample, calculate the expected value and standard deviation of each solvable quantity, and plot the probability density curve and cumulative distribution curve. 105: A step that processes uncertainties within the power grid, such as load fluctuations and uncertainties in new energy output, based on probability density curves and cumulative distribution curves, analyzes and predicts the operational status of the power grid, more accurately reflects the actual state of the power grid, evaluates the performance of the grid under different operating conditions, and contributes to identifying potential weaknesses in the power grid.

[0023] In short, the embodiment of the present invention segments the range of variation of the random input variable selected through steps 101 to 105 above to set up multiple physical sprout solutions, defines each derived semi-analytical solution as a quadratic power series, combines MG-MDHEM based on self-adaptive multiple sprout solutions with parallel multivariate quotient method to solve the power flow solution for each sample in parallel, and finally, through statistical analysis, quickly obtains the stochastic power flow results of the power system, more accurately reflects the actual state of the power system, evaluates the performance of the system under different operating conditions, and identifies potential weaknesses in the power grid.

[0024] (Example 2) The overall computation flow of the embodiment of the present invention is shown in Figure 1, and is divided into an offline analysis part, an online application part, and a statistical analysis part, with parallel acceleration completed by the online application part.

[0025] 1. The offline analysis portion mainly includes a process of solving quadratic semianalytic solutions for each sub-interval segmented from the target quantity using MG-MDHEM based on self-adaptive multiple bud solutions, and in the embodiment of the present invention, this process is called offline analysis.

[0026] 2. The online application portion includes multi-scenario tidal flow calculations, which primarily involve processes such as generating random input samples, converting input samples into embedding variable values, classifying and reducing the embedding variable values ​​of segmented samples, and calculating Padé approximations using parallel multivariate quotient methods. In embodiments of the present invention, this process is referred to as the online application. This essentially involves calculating tidal flow solutions for multi-scenario samples using semi-analytical solutions of the quantities to be solved.

[0027] III. The statistical analysis portion mainly includes calculating the expected value and standard deviation of each solvable quantity, plotting probability density curves and cumulative distribution curves, etc., and in the embodiments of the present invention, this process is called statistical analysis.

[0028] The means of Example 1 will be further explained below with reference to specific calculation formulas and drawings.

[0029] In the offline analysis portion, it is first necessary to construct an AC power flow model of the power system based on MG-MDHEM as follows.

[0030]

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[0031] Next, we solved the above model, that is, calculated the physical sprout solution, and successively derived higher-order power series to obtain the quadratic semianalytic solution of the quantity to be solved as follows.

[0032] A physical sprout is set as the initial value of the solution under operating conditions that have physical significance. Theoretically, it is possible to define a solution in any state as a physical sprout. Physical sprouts can be calculated using conventional HELM, and the calculation procedure is shown in Non-Patent Document 9.

[0033] The recurrence relation for a higher-order power series is as follows:

[0034]

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[0035]

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[0036] The MG-MDHEM proposed in the embodiment of the present invention utilizes the characteristic that physical embryo solutions can be flexibly set, setting multiple initial points in segments within the range of variation of the random input variable, sequentially deriving multiple groups of semianalytical solutions using the solutions at the initial points as physical embryo solutions, and reducing computational cost by defining the order of the semianalytical solutions as quadratic.

[0037] Self-adaptive multiple sprout calculation, that is, by adaptively searching for the convergence interval of the quadratic semianalytic solution of the variable to be solved in the ground state, the segment length of the variation range of the selected random input variable is calculated, and after segmentation, the midpoint of each sub-interval is set as the initial point, and the solution at the initial point is found, thereby realizing self-adaptive calculation of multiple sprouts. The convergence range of the quadratic semianalytic solution of the variable to be calculated in the ground state is searched, and the embedding variable values ​​are updated using a variable step size method based on exponential scaling, and the formula for the variable step size method is as follows.

[0038]

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[0039] The upper and lower bounds of the convergence range of the explored ground state semianalytic solution are defined as s, respectively. max or s min Assuming this, the segment length s b The formula is as follows:

[0040]

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[0041] The number of segments G and the overall upper and lower limits φ of the range of variation for the segments targeted for multiple seedling setting. up , φ low The formula for calculating this is as follows:

[0042]

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[0043] In the online application section, K input random variable samples are generated according to the probability distribution of the random variables, these random variables are converted into embedding variable values, assigned to their respective segment intervals, substituted into the quadratic semianalytic solutions of the solvable quantities for each segmented sub-interval after reduction, and then the steady-state currents are rapidly determined using the parallel multivariate quotient method.

[0044] After converting the random input variable to the value of the embedding variable, it can be assigned to the segment interval to which it belongs via equation (14).

[0045]

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[0046] After assigning the embedded variable values ​​to the intervals to which they belong, it is necessary to reduce these values ​​and then substitute them into the semi-analytical solutions of the quantities to be solved in each sub-interval. The reduction formula is as follows:

[0047]

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[0048] The parallel calculation formula for the multivariate quotient method is as follows:

[0049]

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[0050] The diagonal Padé approximation formula can be expressed as follows after parallelization.

[0051]

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[0052] The specific steps of the embodiment of the present invention are as follows: 201: The process involves reading grid data, setting the convergence precision E of the maximum unequilibrium τ, segmenting the load fluctuation range and setting multiple sprouts according to the wind power penetration rate (if less than 15%), segmenting the wind turbine output fluctuation range and setting multiple sprouts if it exceeds 15%, calculating the physical sprout in the ground state, sequentially deriving its preceding quadratic power series using equations (6) to (9), obtaining a quadratic semianalytic solution in the ground state, and setting the initial value s=0 of the embedding variable as the starting point for exploring the upper and lower bounds. 202: Substitute the embedding variable s into the second-and-a-half-order analytical solution to obtain the Padé approximation. 203: Determine whether the upper or lower bound of the search satisfies the convergence condition. If it does, calculate Δs using equation (11), update the embedded variable value upward or downward, and return to step 202. If it does not satisfy the condition, set the embedded variable value s to the upper bound s of the convergence range. max or lower limit s min Output as follows, proceed to step 204. 204: Segment length s according to formula (12) b Calculate the number of segments G and the overall upper and lower limits φ of the segments according to formula (13), and up and φ low Steps to calculate 205:[φ low ,φ up The interval is segmented, the midpoint of the segmented sub-interval is used as the initial point, and the solution at the initial point is calculated as the physical sprout of each sub-interval. Then, using the physical sprout of each sub-interval as the constant term of a multivariate power series, the quadratic semianalytic solutions of the variables to be calculated for each sub-interval are sequentially found using equations (6) to (9). 206: A step in which K random input samples are generated based on a probability model of uncertain factors, the samples are converted into embedding variable values, assigned to their respective segment intervals according to equation (14), and the embedding variable values ​​are reduced according to equation (15). 207: Substitute the embedded variable values ​​into the semi-analytical solutions of the quantities to be solved in each sub-interval, calculate the Padé approximation for each sample using the parallel multivariate quotient method of equations (16) to (20), and the obtained Padé approximation becomes the tidal current solution. 208: A step to perform statistical analysis, calculate the expected value and standard deviation of each solvable quantity, and plot the probability density curve and cumulative distribution curve of the selected research subject.

[0053] (Example 3) The feasibility of the means of Example 1 and Example 2 will be examined below with reference to Figures 2, 3, and 4, and Tables 1, 2, and 3.

[0054] This embodiment was validated and analyzed using a modified IEEE14 test system. Figure 2 shows the IEEE14 system configuration diagram with a rated capacity 10MW wind power plant at node 7. Considering the randomness of the load and the output of the wind power plant, the load fluctuations follow a normal distribution. The original data for the calculation example was assumed to be the expected value and the standard deviation to be 10% of the expected value. The randomness of the wind speed can be described by a two-parameter Weibull distribution with a shape parameter of 3.97 and a scale parameter of 10.7. The cut-in wind speed of the wind power plant was assumed to be 3 m / s, the rated wind speed was 15 m / s, and the cut-out wind speed was 25 m / s. Constant power control was used, assuming that the power generation of the wind power plant in the ground state is 50% of the rated capacity. We used a 3D MG-MDHEM as an example for verification and analysis. The embedded variable s1 represents the change in load power in area 1 (nodes 4, 9, 10, 13, 14), and s2 represents the change in load power in area 2 (nodes 5, 11, 12). We also assumed that the load power in area 2 does not change, i.e., s2=0, and used the embedded variable s3 to represent the change in output of wind power plant node 7. The number of simulation iterations for the MCS method was selected to be 10,000, and the calculation precision of MG-MDHEM was set to 0.0001.

[0055] To verify the accuracy of the stochastic power flow calculated by the embodiment of the present invention, the results of the stochastic power flow calculation for the IEEE14 test system according to the present invention were compared with those of the conventional NR method-based MCS method. Figure 3 shows the probability distribution curves of the voltage amplitude at node 4 and the active power at branch 4-5. Table 1 shows in detail the expected value, standard deviation, and relative error of the voltage amplitude for some PQ nodes obtained by the two algorithms. Clearly, from Figure 3, the probability distribution curves of the voltage amplitude at node 4 and the active power at branch 4-5 calculated by this method are in almost agreement with those of the conventional MCS method, and there is only a very small error between the two. Furthermore, as can be seen from Table 1, for the expected value and standard deviation of the voltage amplitude of different PQ nodes, the expected value and standard deviation of the node voltage amplitude obtained by this method are all almost equal to those of the conventional MCS method, and the relative error of the expected value was less than 0.01% in all cases. Because the standard deviation is small, the relative error is about 1%, but the measured values ​​are almost the same. The method of the present invention has been verified to have high computational accuracy in stochastic power flow calculations.

[0056] [Table 1]

[0057] To verify the computational efficiency of this method, we compared the computation time of this method with that of an MCS stochastic power flow algorithm based on a different method. The results are shown in Table 2.

[0058] [Table 2] Note: The MDHEM serial method refers to a combination of the conventional MDHEM method and an existing serial multivariate quotient method. The MDHEM parallel method refers to a combination of the conventional MDHEM method and the parallel multivariate quotient method proposed in the embodiment of the present invention. The embodiment of the present invention combines the proposed MG-MDHEM with the parallel multivariate quotient method. All of the above methods require the calculation of stochastic power flow in conjunction with the MCS method.

[0059] As can be seen from the comparison of the required time for MCS stochastic power flow calculations based on different methods in Table 2, the required time for stochastic power flow calculations using the method proposed in the embodiment of the present invention was much shorter than that of the conventional MCS method based on the NR method. The table compares the required time for stochastic power flow calculations combining the conventional MDHEM method and the multivariate quotient method in serial or parallel processing, demonstrating that the parallel multivariate quotient method proposed in the embodiment of the present invention can effectively improve the calculation speed of the Padé approximation. Comparing the time for MDHEM parallel and stochastic power flow calculations using the embodiment of the present invention, the high efficiency of MG-MDHEM proposed in the embodiment of the present invention was verified.

[0060] In short, this self-adaptive multiple-bud MG-MDHEM and parallel multivariate quotient method for calculating stochastic power flow is the most computationally efficient, showing a 92.1-fold improvement in computational efficiency compared to the NR method-based MCS stochastic power flow algorithm. Compared to conventional MCS stochastic power flow algorithms based on serial or parallel MDHEM, this method is also computationally more efficient. As can be seen, this method is more efficient when solving the stochastic power flow of a power system, the calculation results are accurate, and it can adequately realize the calculation of stochastic power flow in a power system.

[0061] [Table 3]

[0062] Table 3 shows a comparison of the order of the power series required for the semi-analytical solutions of conventional MDHEM and MG-MDHEM when calculating stochastic power flow. As can be seen from Table 3, in order to achieve convergence, the order of the semi-analytical solution of MDHEM is greater than 2nd order, which increases the computational cost of solving the power series and the multi-scenario Padé approximation part. Figure 4 is a schematic diagram of the load fluctuation range segments in an example calculation using MG-MDHEM. As can be seen from Figure 4, MG-MDHEM sets two sprout solutions by self-adaptive segmentation, sequentially derives semi-analytical solutions for the two segments, and ensures convergence of the semi-analytical solution for each segment using only a 2nd-order power series. When performing stochastic power flow calculations, the sample size is uniformly set to 10,000, i.e., there are 10,000 sets of embedding variable values. When calculating the Padé approximation, MDHEM requires the calculation of a 3rd-order multivariable power series, while MG-MDHEM only requires the calculation of a 2nd-order multivariable power series, thus effectively reducing the computational cost.

[0063] From the analysis described above, it can be seen that this self-adaptive multiple spore stochastic power flow calculation method based on MG-MDHEM and parallel multivariate quotient method has high computational efficiency and accuracy, and offers clear advantages over conventional MCS stochastic power flow calculation methods.

[0064] As shown in Figure 5, the present invention also relates to a self-adaptive multiple-budded MG-MDHEM stochastic power flow calculation system comprising a data acquisition module, an MG-MDHEM offline analysis module, a stochastic power flow online calculation module, and a weakness identification module.

[0065] The aforementioned data acquisition module is used to store historical data of grid load and wind power output, and to generate K sample data sets by sampling when a random input variable is given a probability distribution. The aforementioned MG-MDHEM offline analysis module is used to set up multiple sprouts by segmenting the range of variation of selected random input variables based on a multidimensional regular embedding method for self-adaptive multiple sprouts, and to sequentially solve the quadratic semianalytic solutions of the node voltages in the sub-intervals of each segment. The stochastic power flow online calculation module calculates semi-analytical solutions of node voltages obtained by the MG-MDHEM offline analysis platform using samples extracted from the data acquisition center, and obtains probability density curves and cumulative distribution curves for each node voltage and branch power. The steps of calculating the probability density curves and cumulative distribution curves for each node voltage and branch power are completed by the Dell PowerEdge R730 server.

[0066] The weakness identification module processes uncertainties within the power grid based on probability density curves and cumulative distribution curves obtained by the stochastic power flow online calculation module. It is used to analyze and predict power grid operation and identify potential weaknesses in the grid. Based on the identified potential weaknesses, operators can take reasonable and feasible control measures to improve the safety of grid operation.

[0067] Those skilled in the art will understand that the attached drawings are merely schematic diagrams of preferred embodiments, and that the above-mentioned embodiment numbers are for descriptive purposes only and do not indicate any superiority or inferiority among the embodiments.

[0068] The foregoing describes only preferred embodiments of the present invention and does not limit the invention. Any modifications, substitutions with equivalents, or improvements made within the spirit and principles of the invention should also be included within the scope of protection of the present invention.

Claims

1. A method for calculating power flow based on multiple buds and multidimensional regular embeddings, Based on a multidimensional regular embedding method for self-adaptive multiple sprouts, the variation range of selected random input variables is segmented to set up multiple sprouts, and the quadratic semianalytic solutions of the node voltages in the sub-intervals of each segment are sequentially solved. The process involves generating K sample groups based on the probability distribution of random input variables, converting the sample data into embedded variable values, and then performing classification and reduction. The steps include substituting the aforementioned embedding variable values ​​into the quadratic semianalytic solution of the node voltage in each sub-interval, calculating Padé approximations in combination with the parallel multivariate quotient method, obtaining the tidal flow solution for each sample, statistically analyzing the tidal flow solution for each sample, calculating the expected value and standard deviation of each solvable quantity, and plotting the probability density curve and cumulative distribution curve, The steps include processing uncertainties within the power grid based on the probability density curve and cumulative distribution curve, analyzing and predicting the operational status of the power grid, and identifying potential weaknesses in the power grid, A method for calculating power flow based on multiple spores and multidimensional regular embeddings, characterized by including the above.

2. The sequential calculation of the quadratic semianalytic solution for the node voltage in the aforementioned sub-section of each segment is as follows: By adaptively searching for the convergence interval of the quadratic semianalytic solution of the solvable quantity in the ground state, the segment length of the variation range of the selected random input variable is calculated. After segmentation, the midpoint of each sub-interval is set as the initial point, and then the solution at the initial point is found, thereby realizing self-adaptive calculation of multiple bud solutions. A method for calculating stochastic power flow based on multiple sprout solutions and multidimensional regular embeddings, as described in claim 1.

3. The method for calculating stochastic power flow based on multiple sprout solutions and multidimensional regular embeddings according to claim 1, characterized in that the search for the convergence interval of the quadratic semianalytic solution of the quantity to be solved in the ground state is performed by updating the embedding variable values ​​using a variable step size method based on exponential scaling. Update formula: [Math 1] In the formula, s ０ λ is the reference value for the step size, τ is the maximum unbalance value of the active power of the PV node, the active power and reactive power of the PQ node, E is the tolerance of the maximum unbalance amount τ, and λ is the amplification coefficient. The upper and lower bounds of the convergence range of the explored ground state semianalytic solution are s, respectively. ｍａｘ or s ｍｉｎ When this is the case, the segment length s ｂ The formula: [Math 2] In the formula, └・┘ represents the round-down function. The number of segments G and the overall upper and lower limits φ of the range of variation for the segments targeted for multiple germination settings. ｕｐ , φ ｌｏｗ The formula for calculation: [Math 3] In the formula, Φ is the percentage of the variation range for the selected multiple bud setting target.

4. Substituting the aforementioned embedding variable values ​​into the quadratic semianalytic solution of the node voltage in each sub-interval and calculating the Padé approximation in combination with the parallel multivariate quotient method is specifically as follows: The random variables are converted to the values ​​of the embedding variables, assigned to their respective segment intervals, and substituted into the quadratic semianalytic solutions of the quantities to be solved for each of the reduced sub-intervals. Then, the K steady-state currents are calculated using the parallel multivariate quotient method, and the calculation formula is: Math 4 【number】 In the formula, s ｇｎ s is the embedded variable value assigned to segment g. ｉ is the embedded variable value after segment target sample transformation, and g is the segment number. The method for calculating probabilistic power flow based on multiple bud solutions and multidimensional regular embeddings according to claim 1, characterized in that the embedding variable values ​​are assigned to the intervals to which they belong, then reduced, and then substituted into the semi-analytical solutions of the quantities to be solved in each sub-interval. Reduction type: [Math 5] where s ｇ０ is the rate of change of the initial point of segment g with respect to the base state, and s ｇｍ is the embedded variable value after reduction.

5. The parallel calculation formula for the multivariate quotient method is as follows, characterized in that it is a stochastic power flow calculation method based on multiple sprouts - multidimensional regular embedding according to claim 1. 【Number 6】 In the formula, QD is the difference quotient table in three dimensions, [q １ （ｍ） ,:] is all the q in all sub-2D matrices in the difference quotient table １ （ｍ） This represents the index, where D is the dimension of the multivariable holomorphic function, s Ｄ n is a vector composed of the embedding variable values ​​of the D-th dimension. Ｄ is Ｄ The degree of the power series, d ｆ and q ｆ These are the terms relating to the difference and the terms relating to the quotient, which appear alternately in the difference quotient table, c[n １ , ..., n Ｄ ] is the coefficient of the multivariable power series, m is the ordinal index of the difference term or quotient term in a column in the difference quotient table, and f is the ordinal index of the difference term or quotient term in a row in the difference quotient table.

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