A power distribution substation three-phase load imbalance treatment method based on FCM time period division and improved NSGA-II algorithm

Abstract

The application provides a power distribution substation three-phase load unbalance treatment method based on FCM period division and improved NSGA-II algorithm, first, according to historical load data, short-term day-ahead load prediction is carried out by using a wavelet denoising regression model, then the obtained load curve prediction result is subjected to control period division based on a fuzzy C-means clustering algorithm (fuzzy C-means, FCM), and then the improved genetic algorithm NSGA-II is used for optimization of commutation switch phase distinction for each control period, so that day-ahead optimization of commutation switch action is realized under the condition of considering the limitation of device action times, the three-phase load balance degree of the substation is maximized. Finally, it is verified by examples that the method of the application can quickly and accurately obtain an optimization scheme, the three-phase unbalance degree of the substation is obviously reduced, and the action times of the commutation switch are effectively limited, the effectiveness and practicability are considered, and the application has practical engineering value.

Description

Technical Field

[0001] This invention relates to the field of three-phase load imbalance management in low-voltage distribution substations, specifically a method for managing three-phase load imbalance in distribution substations based on FCM time period division and an improved NSGA-II algorithm. Background Technology

[0002] my country's low-voltage distribution network has a large number of substations, and its management has historically been relatively extensive. Furthermore, many low-voltage substations have a mixed structure of three-phase and single-phase power, leading to frequent three-phase load imbalances due to the presence of numerous single-phase loads with unbalanced spatial and temporal distribution, as well as the randomness and volatility of electricity user behavior. Three-phase load imbalances can cause numerous problems for the distribution network, such as increased transformer losses, increased line losses, low voltage at the network's endpoints, and reduced power supply quality. Therefore, addressing the three-phase imbalance problem in low-voltage substations is essential to providing users with good power quality and ensuring the economical operation of the power grid.

[0003] Current solutions for three-phase load imbalance involve manually adjusting single-phase load distribution or adding reactive power compensation equipment or devices. Manual adjustment inevitably suffers from lag and increases the workload of maintenance personnel, while reactive power compensation does not fundamentally change the load distribution, requires equipment installation, has high maintenance costs, and cannot achieve continuous regulation. To effectively address three-phase imbalance in low-voltage distribution areas, configuring phase-switching switches to modify user phase sequence is an effective method. With the maturity of intelligent phase-switching switch technology and the reduction in production costs, intelligent phase-switching switches have been gradually promoted, achieving significant economic and management benefits, greatly reducing maintenance workload, and thus improving the efficiency and management level of the distribution network. Although installing phase-switching switches in multiple single-phase high-power load branches in the distribution area can achieve three-phase load adjustment, the limited number of switch operations is often overlooked, leading to varying degrees of reduction in switch lifespan and efficiency. Furthermore, traditional three-phase imbalance mitigation methods based on intelligent commutator switches only optimize and adjust unbalanced loads in certain areas or during certain times within a transformer substation. They have limitations when facing complex load conditions across the entire substation or throughout the day, failing to effectively and reasonably pre-process unbalanced loads and thus failing to achieve significant mitigation results. Therefore, it is necessary to improve existing three-phase imbalance mitigation methods based on commutator switches. Summary of the Invention

[0004] To address various problems in traditional three-phase imbalance management methods, reduce labor costs and the possibility of human error, and improve the accuracy and efficiency of distribution area load imbalance regulation while considering the limitation on the number of phase switching operations, this invention provides a distribution area three-phase load imbalance management method based on FCM time period division and an improved NSGA-II algorithm.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for managing three-phase load imbalance in distribution substations based on FCM time period division and an improved NSGA-II algorithm includes the following steps:

[0007] Step 1: Based on known historical load data, a load prediction model is established using an improved wavelet transform and Mallat algorithm. The input data is preprocessed using the prediction model to suppress noise signals while retaining the main features of the curve. Then, the day-ahead short-term load prediction for each user in the distribution area is achieved through supervised learning, resulting in the short-term day-ahead load prediction curve.

[0008] Step 2: Based on the short-term daytime load forecast curve obtained in Step 1, the whole day is divided into several consecutive control periods using the fuzzy C-means clustering algorithm. That is, periods with similar load conditions are divided into a longer control period. Within a control period, the phase switch maintains one phase, while the phase of the phase switch is adjusted between adjacent control periods.

[0009] Step 3: Optimize each control period segment divided in Step 2 separately, that is, determine which phase of each switch is switched to, i.e., the phase of the switching switch is optimized by using the improved NSGA-II genetic algorithm to obtain the phase of each switching switch in each control period more quickly and accurately, so as to obtain the optimal phase optimization scheme for each period.

[0010] Step 4: Based on the optimal phase optimization scheme for each time period in Step 3, form the day-ahead plan for the entire distribution area, and finally send it to each commutation switch terminal via carrier or wireless communication to achieve three-phase load balance control.

[0011] Furthermore, Step 1 includes the following specific steps:

[0012] Step 1.1: Collect the load power of n single-phase load branches within the area, sampling once every 1 hour to form a historical load power array D for 24 hours. P =[P1, P2, ..., P n ], where P1 to P n A load power array of length 24 for each sampling point;

[0013] Step 1.2: Use discrete wavelet transform to process the above historical load power array D. P The data is processed and decomposed to obtain detail coefficients. and approximation coefficients ;

[0014] (1)

[0015] In the formula: i takes values ​​from 1 to n; e takes integer values ​​from 1 to 24; This represents the value of the i-th historical load power data at time e; These are wavelet coefficients, typically taken as... .

[0016] Step 13: Apply the Birge-Massart hierarchical soft thresholding strategy to the detail coefficients after wavelet decomposition in Step 1.2. and approximation coefficients After noise reduction processing, the detail coefficients and approximation coefficients are obtained as follows:

[0017] (2)

[0018] In the formula: This is an empirical coefficient, ranging from 2 to 4;

[0019] Step 1.4: Construct a load forecasting model y using the Mallat algorithm. ie :

[0020] (3)

[0021] Step 1.5: Supervised learning of the denoised load curve model from Step 1.4 is performed using the LSRT weak learner to obtain the short-term day-ahead load forecast curve P. load :

[0022] (4)

[0023] (5)

[0024] In the formula: This represents the short-term day-ahead load forecast data obtained from n data collection points.

[0025] Furthermore, in Step 2, the fuzzy C-means clustering algorithm is used to divide the entire day into several consecutive control periods. The specific steps are as follows:

[0026] Step 2.1: Assume that m phase-change switches are installed at single-phase load users within the distribution area, and no phase-change switches are installed at the remaining nm locations. Based on whether phase-change switches are installed, the load within the distribution area can be divided into adjustable loads and non-adjustable loads. Based on the load forecast data P... load The single-phase load users in the distribution area equipped with phase-change switches are formed into a load matrix with m columns and 24 rows, and their column vectors are denoted as P. s1 P s2 ... P sm The subscript 's' represents P. load The data includes load power data with phase-change switches installed, with each vector containing 24 load power values; non-adjustable loads, i.e., the total load of users without phase-change switches, correspond to phases a, b, and c, P. load The remaining nm load data can be aggregated to form three column vectors P. a0 P b0 P c0 Each vector also contains 24 load power values; the total load matrix is ​​composed of the above two types of load matrices, denoted as P. L The dimension of the matrix is ​​24×(3+m);

[0027] Step 2.2: Add a new dimension indicator, introducing a time column vector t=[1 2 … 24] T The load power matrix P described in step 2.1 L The time column vectors are normalized respectively to obtain and as follows:

[0028] (6)

[0029] In the formula: q takes an integer between 1 and (3+m); and Represent matrix P respectively L Find the maximum and minimum values ​​of the data in the q-th column. Combine these values ​​into a data matrix. The dimension of this matrix is ​​24×(4+m);

[0030] Step 2.3: Introduce correction coefficients For the time vector in step 2.2 To perform magnification processing, that is The aim is to enhance the influence of the time vector dimension during the classification process, so that adjacent time periods are more effectively clustered into one class. Initialization Make it equal to 1;

[0031] Step 2.4, with As input for FCM clustering, let array A = {A1, A2, ..., A...}R} represents the array formed by the boundary times of R time periods within a 24-hour period of a day. Output the membership matrix X. jk and cluster center V k as follows:

[0032] (7)

[0033] in:

[0034] (8)

[0035] In the formula: Used to measure Data in column j and row p With the center point of class k The distance between them, j and k range from 1 to (m+4), p=j+2; b is a weighting parameter, which ranges from 1 to 5;

[0036] If k+1>R, then let = + And re-enter F * Perform calculations, where Take a value between 1.5 and 2; otherwise, determine the value based on the membership matrix X. jk and cluster center V k Directly output the segmented results The division of the control period ends:

[0037] (9)

[0038] In the formula: Represents the first time interval in R time periods. Each time period; Indicates the first If the number of timing segments of the commutator switching action within a given day is R, then the FCM algorithm can divide the 24 time periods into R segments, and the time corresponding to each time period forms an array A.

[0039] Furthermore, in Step 3, an improved NSGA-II genetic algorithm is used to optimize the phases connected to the commutation switch in each time period. The specific steps are as follows:

[0040] Step 3.1, Gene Encoding: For the m commutator switches configured in the distribution area, the corresponding gene encoding for each time period consists of m integers, represented as w=[w s1 w s2 … w smThe code, where each bit represents the phase a, b, and c connected to the commutator switch (1, 2, 3 respectively), calculates the three-phase load for each time period based on the code. The calculation formula is as follows:

[0041] (10)

[0042] In the formula: , , Indicates the t-th i The total three-phase load of all load points on the power distribution line during a given time period; t i Indicates the time period number; , , Indicates the t-th i The total load of each phase (a, b, c) of the non-adjustable load branch during each time period; Indicates the t-th i The single-phase load corresponding to the j-th phase switch in the time period;

[0043] Step 3.2: Set the objective function: Based on the three-phase load conditions of the distribution substation, define the three-phase imbalance as:

[0044] (11)

[0045] In the formula: Indicates the t-th i Three-phase imbalance over a given period; , and They represent the t-th i The maximum, minimum, and average values ​​of the total three-phase load of the distribution transformer area lines during each time period;

[0046] The optimization goal is set as follows:

[0047] (12)

[0048] Where: minf k The objective function for the k-th control period is denoted by t; x t y These represent the start and end times of the corresponding control period in array A;

[0049] Step 3.3: Using the NSGA-II algorithm, solve the objective function to obtain the gene coding w for each time period. The NSGA-II algorithm provides the following computational parameters: population size N, maximum crossover rate p. cmax Minimum crossover rate p cmin Maximum number of iterations Cmax And the simulated annealing initial temperature T0, cooling coefficient Returns the number of times K, where the values ​​of the above parameters range from 100 to 300. cmax =0~1, p cmin =0~1、C max =R, T0 = 0~200, =0~1.5, K=1;

[0050] The above calculations are repeated using the above method to obtain the gene code w of each commutator switch in the corresponding time period for all R time periods of a 24-hour day. This determines the daytime commutation plan of m commutators switches in each time period. When the corresponding gene code is 1 in a certain time period, it means that it is connected to phase a, 2 means it is connected to phase b, and 3 means it is connected to phase c.

[0051] Furthermore, Step 4, based on the optimal phase-specific optimization scheme for each time period in Step 3, forms the overall day-ahead plan for the entire distribution area, and finally sends it to each commutation switch terminal via carrier wave or wireless communication to achieve three-phase load balance control. The specific steps are as follows:

[0052] Based on the phase switching plan formed before the day of the phase switching, the plan is imported into the intelligent fusion terminal of the distribution area. Finally, the intelligent fusion terminal of the distribution area sends switching commands to each phase switching terminal through carrier or wireless communication to realize the three-phase load balance control of the distribution area.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] The control period segmentation method proposed in this invention can cluster periods with similar load levels and temporal proximity, thereby dividing the entire day into several consecutive control periods. An improved genetic algorithm can obtain the optimal phase of the switching switches in each control period, thus enabling faster and more accurate acquisition of the optimal phase adjustment scheme for power users in the distribution network area. The method proposed in this invention can provide precise decision support for the management of three-phase load imbalance in distribution networks, significantly reducing the three-phase imbalance and effectively limiting the number of switching switch operations, balancing effectiveness and practicality. This invention's method can optimize switching switch operations from the perspective of the entire day's cycle, demonstrating significant practical value. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a code diagram of the LSRT learner algorithm provided in an embodiment of the present invention;

[0057] Figure 2 This is a flowchart of the overall method proposed in this invention;

[0058] Figure 3 This is a diagram of the low-voltage distribution substation topology provided in Embodiment 1 of the present invention;

[0059] Figure 4 This is a graph showing the predicted daily load curve of a three-phase non-adjustable load provided in Embodiment 1 of the present invention;

[0060] Figure 5 This is a diagram of the FCM clustering results provided in Embodiment 1 of the present invention;

[0061] Figure 6 This is a three-phase load curve diagram optimized based on the method of the present invention, provided in Embodiment 1 of the present invention;

[0062] Figure 7 This is a three-phase load curve diagram with independent optimization for each time period provided in Embodiment 1 of the present invention;

[0063] Figure 8 This is a comparison diagram of the imbalance before and after commutation optimization provided in Embodiment 1 of the present invention;

[0064] Figure 9 This is a comparison chart of the number of commutation switch operations provided in Embodiment 1 of the present invention;

[0065] Figure 10 This is a graph showing the predicted daily load curve of a three-phase non-adjustable load provided in Embodiment 2 of the present invention;

[0066] Figure 11 This is a diagram of the FCM clustering results provided in Embodiment 2 of the present invention;

[0067] Figure 12 This is the imbalance diagram after commutation optimization provided in Embodiment 2 of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] The specific LSRT learner algorithm code is as follows: Figure 1 As shown. LSRT, also known as Least Squares Regression Tree, is a mathematical optimization technique. It finds the best function match for data by minimizing the sum of squared errors. Least squares can be used to easily obtain unknown data and minimize the sum of squared errors between the obtained data and the actual data. Least squares can also be used for curve fitting. In supervised learning, if the predicted variable is discrete, it is called classification (such as decision trees, support vector machines, etc.); if the predicted variable is continuous, it is called regression. Least squares is the basic method for solving regression problems. This invention uses a least squares regression tree learner to learn and calculate the load prediction curve after noise reduction, thereby reducing the impact of load curve fluctuations and facilitating subsequent time period segmentation steps.

[0070] As shown in Figure 2, this embodiment of the invention provides a method for managing three-phase load imbalance in distribution substations based on FCM time period division and an improved NSGA-II algorithm, comprising the following steps:

[0071] Step 1: Based on known historical load data, a load forecasting model is established using an improved wavelet transform and Mallat algorithm. This model can preprocess the input data, suppress noise signals, and retain the main features of the curve. Then, through supervised learning, the day-ahead short-term load forecast of each user in the distribution area is realized, and the short-term day-ahead load forecast curve is obtained.

[0072] Step 2: Based on the daily load curve prediction results obtained in Step 1, the entire day is divided into several consecutive control periods using the fuzzy C-means (FCM) clustering algorithm. That is, periods with similar load conditions are divided into a longer control period. Within a control period, the phase switching switch maintains one phase, while the phase switching switch is adjusted between adjacent control periods. This ensures that the number of control periods is less than the maximum number of times the equipment can operate, thus avoiding exceeding the limit for the number of switch operations.

[0073] Step 3: Optimize each time period divided in Step 2 separately, that is, determine which phase of a, b, and c each switch switches to. Since the phase is discrete, the improved NSGA-II genetic algorithm is used to optimize the phase of the switching switch to obtain a set of optimal results more quickly and accurately, that is, the phase of each switching switch in each control period, so as to obtain the optimal phase optimization scheme for each time period.

[0074] Step 4: Based on the optimization scheme in Step 3, form the day-ahead plan for the entire distribution area, and finally send it to each phase switching terminal via carrier or wireless communication to achieve three-phase load balance control.

[0075] Furthermore, the specific steps for load forecasting in Step 1 are as follows:

[0076] The load in low-voltage distribution substations is typically dominated by residential load, which exhibits significant randomness and volatility, resulting in low accuracy of traditional prediction models. To provide effective and accurate load information for subsequent optimization algorithms and reduce the impact of load curve fluctuations, an improved wavelet transform and Mallat algorithm are used to achieve load forecasting.

[0077] Step 1.1: Collect the load power of n single-phase load branches within the area, sampling once every 1 hour to form a historical load power array D for 24 hours. P =[P1, P2, ..., P n ], where P1 to P n A load power array with a length of 24 for each sampling point.

[0078] Step 1.2: Use discrete wavelet transform to process the above historical load power array D. P The data is processed and decomposed to obtain detail coefficients. and approximation coefficients .

[0079] (1)

[0080] In the formula: i takes values ​​from 1 to n; e takes integer values ​​from 1 to 24; This represents the value of the i-th historical load power data at time e; These are wavelet coefficients, typically taken as... .

[0081] Step 1.3: To reduce the impact of random fluctuations while preserving the overall trend characteristics of the load curve, the Birge-Massart hierarchical soft thresholding strategy is used to refine the detail coefficients after wavelet decomposition in Step 2. and approximation coefficients After noise reduction processing, the detail coefficients and approximation coefficients are obtained as follows:

[0082] (2)

[0083] In the formula: This is an empirical coefficient, which can generally be taken as 2 to 4.

[0084] Step 1.4: Construct a load forecasting model y using the Mallat algorithm. ie .

[0085] (3)

[0086] Step 1.5: Supervised learning of the denoised load curve model from Step 4 is performed using a LSRT (least-squares regression tree) weak learner to obtain the short-term day-ahead load forecast curve P. load .

[0087] (4)

[0088] (5)

[0089] In the formula: This represents the short-term day-ahead load forecast data obtained from n data collection points.

[0090] Furthermore, Step 2 employs the fuzzy C-means clustering algorithm for time period segmentation. The specific steps are as follows:

[0091] Step 2.1: Assume that m phase-change switches are installed at single-phase load users within the distribution area, and the remaining nm locations do not have phase-change switches installed (total load number minus the load number with installed switches). Based on whether phase-change switches are installed, the load within the distribution area can be divided into adjustable loads and non-adjustable loads. Based on the load forecast data P... load The single-phase load users in the distribution area equipped with phase-change switches can be formed into a load matrix with m columns and 24 rows, and the column vectors are denoted as P. s1 P s2 ... P sm The subscript 's' represents P. load The data includes load power data with phase-change switches installed, with each vector containing 24 load power values ​​(hourly load data over 24 hours); non-adjustable loads are the total loads of users without phase-change switches, corresponding to phases a, b, and c, P. load The remaining nm load data can be aggregated to form three column vectors P. a0 P b0 P c0 Each vector also contains 24 load power values. The complete load matrix is ​​composed of these two types of load matrices, denoted as P. L The matrix dimension is 24×(3+m).

[0092] Step 2.2: Add a new dimension indicator, introducing a time column vector t=[1 2 … 24] T The load power matrix P described in step one L The time column vectors are normalized respectively to obtain and as follows:

[0093] (6)

[0094] In the formula: q takes an integer between 1 and (3+m); and Represent matrix P respectively L Find the maximum and minimum values ​​of the data in the q-th column. Combine these values ​​into a data matrix. The dimension of this matrix is ​​24×(4+m).

[0095] Step 2.3: Introduce correction coefficients For the time vector in step two To perform magnification processing, that is This aims to enhance the influence of the time vector dimension during the classification process, enabling adjacent time periods to be clustered into one class more effectively. Initialization Make it equal to 1.

[0096] Step 2.4, with As input for FCM clustering, let array A = {A1, A2, ..., A...} R} represents the array formed by the boundary times of R time periods within a 24-hour period of a day. Output the membership matrix X. jk and cluster center V k as follows:

[0097] (7)

[0098] in:

[0099] (8)

[0100] In the formula: Used to measure Data in column j and row p With the center point of class k The distance between them, j and k range from 1 to (m+4), p=j+2; b is a weighting parameter, which is generally taken from 1 to 5.

[0101] If k+1>R, then let = + And re-enter F * Perform calculations ( (Generally, the value is taken as 1.5~2); otherwise, it is determined according to the membership matrix X. jk and cluster center V k Directly output the segmented results The division of the control period ends.

[0102] (9)

[0103] In the formula: Represents the first time interval in R time periods. Each time period; Indicates the first The time intervals correspond to the time points. If the number of timing segments of the commutator switching action within a given day is R, then the FCM algorithm can divide the 24 time intervals into R segments, and the time points corresponding to each time interval can form an array A.

[0104] Furthermore, Step 3 employs an improved NSGA-II genetic algorithm to optimize the phases connected to the commutation switch in each time period:

[0105] Step 3.1, Gene Encoding. For the m commutator switches configured in the transformer area, the corresponding gene encoding for each time period consists of m integers, which can be represented as w=[w s1 w s2 … w sm The code, where each bit represents the phase connected to the commutator (phases a, b, and c), is 1, 2, or 3 respectively. The three-phase load for each time period can be calculated based on the code, using the following formula:

[0106] (10)

[0107] In the formula: , , Indicates the t-th i The total three-phase load of all load points on the power distribution line during a given time period; t i Indicates the time period number; , , Indicates the t-th i The total load of each phase (a, b, c) of the non-adjustable load branch during each time period; Indicates the t-th i The single-phase load corresponding to the j-th phase switch in the given time period.

[0108] Step 3.2, Objective Function. Based on the three-phase load conditions of the distribution substation area, the three-phase imbalance is defined as:

[0109] (11)

[0110] In the formula: Indicates the t-th i Three-phase imbalance over a given period; , and They represent the t-th i The maximum, minimum, and average total three-phase load of the distribution transformer area lines during each time period.

[0111] The optimization goal is set as follows:

[0112] (12)

[0113] Where: minf k The objective function for the k-th control period is denoted by t; x t y These represent the start and end times of the corresponding control period in array A.

[0114] Step 3.3: Using the NSGA-II algorithm, solve the above objective function to obtain the gene coding w for each time period. The NSGA-II algorithm provides the following computational parameters: population size N, maximum crossover rate p. cmax Minimum crossover rate p cmin Maximum number of iterations C max And the simulated annealing initial temperature T0, cooling coefficient Returns the number of times K. (The values ​​of the above parameters are generally in the range of: N=100~300, p...) cmax =0~1, p cmin =0~1、C max =R, T0 = 0~200, =0~1.5, K=1)

[0115] The above calculations are repeated using the above method to obtain the gene code w of each commutator switch in the corresponding time period for all R time periods of a 24-hour day. This allows us to determine the daytime commutation plan of the m commutators in each time period. When the corresponding gene code is 1 in a certain time period, it means that it is connected to phase a, 2 means it is connected to phase b, and 3 means it is connected to phase c.

[0116] Furthermore, based on the optimized scheme, a day-ahead phase switching plan for the entire distribution area is formulated. This plan is then imported into the intelligent fusion terminal of the distribution area, which finally sends switching commands to each phase switching terminal via carrier wave or wireless communication to achieve three-phase load balance control of the distribution area.

[0117] Example 1:

[0118] To verify the effectiveness and superiority of the method of this invention, this section uses measured data from a certain low-voltage distribution area as an example for simulation verification. The topology of this low-voltage distribution area is as follows: Figure 4As shown, the distribution transformer capacity is 400 kVA, and each line segment is 50 m long; the self-impedance is 0.650 + j0.412 Ω / km; the mutual impedance is 0.01 times the self-impedance. The low-voltage distribution transformer area has 62 users, of which 12 users do not have phase-changing switches installed, and 10 single-phase users on branch lines have phase-changing switches installed. Before the treatment, the three-phase imbalance was generally above 40% throughout the day, with the maximum phase three-phase load imbalance reaching 82.43%, and the initial phases are shown in Table 1.

[0119] Table 1 Initial phase and predicted peak load for each commutator switch

[0120]

[0121] The first step is to perform wavelet transform on the historical load data of this transformer area to decompose the instantaneous anomalies in the normal signal into detail coefficients. and approximation coefficients After denoising using the Birge-Massart hierarchical soft thresholding strategy, the following results were obtained. , Then, the load forecasting model is obtained according to equation (3). Finally, the daily load curve prediction results of the three-phase non-adjustable load in the low-voltage distribution area were obtained by supervised learning using the LSRT learner, as shown in Figure 4. The prediction results of the adjustable load with the phase switching installed are shown in Table 1.

[0122] The second step is to divide the load forecast results obtained in the first step into FCM control periods. Initialization And The data is used as input for clustering, resulting in a membership matrix X. jk =[0.67, 0.89, ..., 1.04], cluster center V k like Figure 5 As shown in the figure, the classification sequences corresponding to each time period are obtained as shown in Table 2.

[0123] Table 2 Comparison of Control Period Division Results

[0124]

[0125] Furthermore, to highlight the superiority of the time-segmentation method proposed in this invention, the time-segmentation results of three methods were compared. Method 1 directly clusters based on the daily load curve; Method 2 considers adding a time vector as a feature index for clustering; and Method 3, the method of this invention, further considers adding a correction coefficient for the time vector for clustering. With a classification number of 5, the results of time-segmentation using the three methods are compared in Table 2. It can be seen that although all three methods divide the 24 time periods into 5 classes, Method 1 and Method 2 clearly show discontinuities in the time periods after classification. Method 2, by adding a time vector, improves upon Method 1, but still results in more segments than the given value. Method 3, by iteratively increasing the correction coefficient of the time vector, highlights the aggregation of adjacent time periods, thereby ensuring the continuity of the time-segmentation and maintaining similar load levels.

[0126] The third step involves optimizing the algorithm using the improved NSGA-II algorithm based on the time segmentation results from the second step. The given computational parameters for the algorithm are: population size N=100, maximum crossover rate p. cmax =0.85, minimum crossover rate p cmin =0.60, Maximum number of iterations C max =200, initial temperature T0=100 and cooling coefficient =0.80. The optimization result U is shown in Table 3.

[0127] Table 3 Optimization results of the improved genetic algorithm

[0128]

[0129] The optimized three-phase load curves based on the method of this invention are shown in Figure 6. Simultaneously, the results of independent optimization for each time period are compared. That is, each hour uses the improved NSGA-II to optimize the optimal phase of the commutator switch without dividing the time period, ensuring that the load in each hour reaches the most balanced state. The corresponding three-phase load curves are shown in Figure 8. A comparison of Figures 4 and 6 shows that after optimizing the commutator switch operation using the method of this invention, the three-phase load curves are significantly closer than before commutation. However, it can also be seen that the load curve of phase c has relatively large fluctuations in the fourth control period (i.e., period 14 to period 18), showing a significant difference from the load curves of the other two phases. This is because the method of this invention sacrifices the similarity of the loads to ensure the continuity of the time periods during the clustering and segmentation process. As shown in Figure 7, independent optimization for each time period ensures that the commutator switches are in the optimal combination for each time period, thus making the three-phase load curves closer. In the first half of the curve, because the unadjustable load of phase b is high, there is still a certain deviation from the other two phases after commutation optimization. Then, the unbalance index f for each time period under three conditions is calculated according to equation (11). k Quantitative analysis was performed, and the comparison is shown in Figure 8. Figure 8 shows that the overall three-phase imbalance is relatively high without commutation. After commutation optimization, the three-phase imbalance value significantly decreased. The imbalance was lowest when optimized independently in each time period. The method of this invention also achieved satisfactory results in most time periods. However, due to the limitation on the number of commutation switch operations, the three-phase imbalance did not decrease or even slightly increased in some time periods. This is a concession made for considering the overall situation. The number of commutation switch operations corresponding to the two optimization results was statistically analyzed, for example... Figure 9 As shown, although independent optimization of each time period can ensure the lowest imbalance in each time period, it may cause frequent operation of the commutation switches, which is inconsistent with actual needs. The method of the present invention optimizes based on the division of control time periods, dividing the whole day into 5 control time periods. The maximum number of operations of each commutation switch in the whole day is limited to 5 times. Some switches are planned to operate less than 5 times. It can be seen that the method of the present invention ensures that the number of operations of each switch can be effectively limited, thereby extending the service life of the equipment.

[0130] Example 2: The low-voltage distribution transformer area topology is consistent with Example 1. The number of users in the low-voltage distribution transformer area is 62, of which 7 users do not have phase-changing switches installed, and 11 single-phase users on branch lines have phase-changing switches installed. Before the treatment, the three-phase imbalance was generally above 50% throughout the day, and the maximum three-phase load imbalance reached 89.64%, as shown in Table 4.

[0131] Table 4 Initial phase and predicted peak load for each commutator switch

[0132]

[0133] The first step is to perform wavelet transform on the historical load data of this transformer area to decompose the instantaneous anomalies in the normal signal into detail coefficients. and approximation coefficients After denoising using the Birge-Massart hierarchical soft thresholding strategy, the following results were obtained. , Then, the load forecasting model is obtained according to equation (3). Finally, the daily load curve prediction results of the three-phase non-adjustable load in the low-voltage distribution area were obtained by supervised learning using the LSRT learner, as shown in Figure 11. The prediction results of the adjustable load with the phase switching installed are shown in Table 4.

[0134] The second step is to divide the load forecast results obtained in the first step into FCM control periods. Initialization And The data is used as input for clustering, resulting in a membership matrix X. jk =[0.64, 0.98, ..., 1.54], cluster center V k like Figure 11 As shown in the figure, the classification sequences corresponding to each time period are obtained as shown in Table 5.

[0135] Table 5 Comparison of Control Period Division Results

[0136]

[0137] The third step involves optimizing the algorithm using the improved NSGA-II algorithm based on the time segmentation results from the second step. The given computational parameters for the algorithm are: population size N=100, maximum crossover rate p. cmax =0.85, minimum crossover rate p cmin =0.60, Maximum number of iterations C max =200, initial temperature T0=100 and cooling coefficient =0.80. The optimization result U is shown in Table 6.

[0138] Table 6 Optimization results of the improved genetic algorithm

[0139]

[0140] Then, the imbalance index f for each time period under the three conditions is calculated according to equation (11). k Quantitative analysis was performed, as shown in Figure 12.

[0141] In summary, the method of the present invention can significantly reduce the three-phase imbalance and effectively limit the number of times the commutator switches operate, thus balancing effectiveness and practicality. The method of the present invention can optimize the operation of the commutator switches from the perspective of the entire day cycle, and has certain practical value.

[0142] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for managing three-phase load imbalance in distribution substations based on FCM time period division and an improved NSGA-II algorithm, characterized in that, Includes the following steps: Step 1: Based on known historical load data, a load prediction model is established using an improved wavelet transform and Mallat algorithm. The input data is preprocessed using the prediction model to suppress noise signals while retaining the main features of the curve. Then, the day-ahead short-term load prediction for each user in the distribution area is achieved through supervised learning, resulting in the short-term day-ahead load prediction curve. Step 2: Based on the short-term daytime load forecast curve obtained in Step 1, the whole day is divided into several consecutive control periods using the fuzzy C-means clustering algorithm. That is, periods with similar load conditions are divided into a longer control period. Within a control period, the phase switch maintains one phase, while the phase of the phase switch is adjusted between adjacent control periods. Step 3: Optimize each control period segment divided in Step 2 separately, that is, determine which phase of each switch is switched to, i.e., the phase of the switching switch is optimized by using the improved NSGA-II genetic algorithm to obtain the phase of each switching switch in each control period more quickly and accurately, so as to obtain the optimal phase optimization scheme for each period. Step 4: Based on the optimal phase optimization scheme for each time period in Step 3, form the day-ahead plan for the entire distribution area, and finally send it to each commutation switch terminal via carrier or wireless communication to achieve three-phase load balance control.

2. The method for managing three-phase load imbalance in distribution substations based on FCM time period division and improved NSGA-II algorithm as described in claim 1, characterized in that, Step 1 includes the following specific steps: Step 1.1: Collect the load power of n single-phase load branches within the area, sampling once every 1 hour to form a historical load power array D for 24 hours. P =[P1, P2, ..., P n ], where P1 to P n A load power array of length 24 for each sampling point; Step 1.2: Use discrete wavelet transform to process the above historical load power array D. P The data is processed and decomposed to obtain detail coefficients. and approximation coefficients ; （1）； In the formula: i ranges from 1 to n; e is an integer from 1 to 24; This represents the value of the i-th historical load power data at time e; For wavelet coefficients, take ; Step 13: Apply the Birge-Massart hierarchical soft thresholding strategy to the detail coefficients after wavelet decomposition in Step 1.

2. and approximation coefficients After noise reduction processing, the detail coefficients and approximation coefficients are obtained as follows: （2）； In the formula: This is an empirical coefficient, ranging from 2 to 4; Step 1.4: Construct a load forecasting model y using the Mallat algorithm. ie : （3）； Step 1.5: Supervised learning of the denoised load forecasting model from Step 1.4 is performed using the LSRT weak learner to obtain the short-term day-ahead load forecast curve P. load : （4）； （5）； In the formula: This represents the short-term day-ahead load forecast data obtained from n data collection points.

3. The method for managing three-phase load imbalance in distribution substations based on FCM time period division and improved NSGA-II algorithm as described in claim 1, characterized in that, In Step 2, the fuzzy C-means clustering algorithm is used to divide the entire day into several consecutive control periods. The specific steps are as follows: Step 2.1: Assume that m phase-change switches are installed at single-phase load users within the distribution area, and no phase-change switches are installed at the remaining nm locations. Based on whether phase-change switches are installed, the load within the distribution area can be divided into adjustable loads and non-adjustable loads. Based on the load forecast data P... load The single-phase load users in the distribution area equipped with phase-change switches are formed into a load matrix with m columns and 24 rows, and their column vectors are denoted as P. s1 P s2 ... P sm The subscript 's' represents P. load The data includes load power data with phase-change switches installed, with each vector containing 24 load power values; non-adjustable loads, i.e., the total load of users without phase-change switches, correspond to phases a, b, and c, P. load The remaining nm load data can be aggregated to form three column vectors P. a0 P b0 P c0 Each vector also contains 24 load power values; the total load matrix is ​​composed of the above two types of load matrices, denoted as P. L The dimension of the matrix is ​​24×(3+m); Step 2.2: Add a new dimension indicator, introducing a time column vector t=[1, 2, ..., 24]. T The load power matrix P described in step 2.1 L The time column vectors are normalized respectively to obtain and as follows: （6）； In the formula: q takes an integer between 1 and (3+m); and Represent matrix P respectively L Find the maximum and minimum values ​​of the data in the q-th column, and combine them into a data matrix. The dimension of this matrix is ​​24×(4+m); Step 2.3: Introduce correction coefficients For the time vector in step 2.2 To perform magnification processing, that is The aim is to enhance the influence of the time vector dimension during the classification process, so that adjacent time periods are more effectively clustered into one class. Initialization Make it equal to 1; Step 2.4, with As input for FCM clustering, let array A = {A1, A2, ..., A...} R } represents the array formed by the boundary times of R time periods within a 24-hour period of a day. Output the membership matrix X. jk and cluster center V k as follows: （7）； in: （8）； In the formula: Used to measure Data in column j and row p With the center point of class k The distance between them, j and k range from 1 to (m+4); b is a weighting parameter, which ranges from 1 to 5; If k+1>R, then let = + And re-enter F * Perform calculations, where Take a value between 1.5 and 2; otherwise, determine the value based on the membership matrix X. jk and cluster center V k Directly output the segmented results The division of the control period ends: （9）； In the formula: Represents the first time interval in R time periods. Each time period; Indicates the first If the number of timing segments of the commutator switching action within a given day is R, then the FCM algorithm can divide the 24 time periods into R segments, and the time corresponding to each time period forms an array A.

4. The method for managing three-phase load imbalance in distribution substations based on FCM time period division and improved NSGA-II algorithm according to claim 1, characterized in that, In Step 3, an improved NSGA-II genetic algorithm is used to optimize the phases connected to the commutation switch in each time period. The specific steps are as follows: Step 3.1, Gene Encoding: For the m commutator switches configured in the distribution area, the corresponding gene encoding for each time period consists of m integers, represented as w=[w s1 w s2 … w sm The code, where each bit represents the phase a, b, and c connected to the phase switch (1, 2, 3 respectively), calculates the three-phase load for each time period based on the code. The calculation formula is as follows: （10）； In the formula: , , Indicates the t-th i The total three-phase load of all load points on the power distribution line during a given time period; t i Indicates the time period number; , , Indicates the t-th i The total load of each phase (a, b, c) of the non-adjustable load branch during each time period; Indicates the t-th i The single-phase load corresponding to the j-th phase switch in the time period; Step 3.2: Set the objective function: Based on the three-phase load conditions of the distribution substation, define the three-phase imbalance as: （11）； In the formula: Indicates the t-th i Three-phase imbalance over a given period; , and They represent the t-th i The maximum, minimum, and average values ​​of the total three-phase load of the distribution transformer area lines during each time period; The optimization goal is set as follows: （12）； Where: minf k The objective function for the k-th control period is denoted by t; x t y These represent the start and end times of the corresponding control period in array A; Step 3.3: Using the NSGA-II algorithm, solve the objective function to obtain the gene coding w for each time period. The NSGA-II algorithm provides the following computational parameters: population size N, maximum crossover rate p. cmax Minimum crossover rate p cmin Maximum number of iterations C max And the simulated annealing initial temperature T0, cooling coefficient Returns the number of times K, where the values ​​of the above parameters range from 100 to 300. cmax =0~1, p cmin =0~1、C max =R, T0 = 0~200, =0~1.5, K=1; The above calculations are repeated using the above method to obtain the gene code w of each commutator switch in the corresponding time period for all R time periods of a 24-hour day. This determines the daytime commutation plan of m commutators switches in each time period. When the corresponding gene code is 1 in a certain time period, it means that it is connected to phase a, 2 means it is connected to phase b, and 3 means it is connected to phase c.

5. A method for managing three-phase load imbalance in distribution substations based on FCM time period division and an improved NSGA-II algorithm, as described in claim 4, is characterized in that... Step 4, based on the optimal phase optimization scheme for each time period in Step 3, forms the overall day-ahead plan for the entire distribution area. Finally, it is transmitted to each commutator terminal via carrier wave or wireless communication to achieve three-phase load balancing control. The specific steps are as follows: Based on the phase switching plan formed before the day of the phase switching, the plan is imported into the intelligent fusion terminal of the distribution area. Finally, the intelligent fusion terminal of the distribution area sends switching commands to each phase switching terminal through carrier or wireless communication to realize the three-phase load balance control of the distribution area.

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