A power line loss analysis system and method based on big data
By using Spearman's rank correlation coefficient and exponential smoothing residual method based on big data analysis, the real-time and accuracy problems of traditional line loss analysis methods are solved, realizing real-time and accurate analysis of power line losses and improving the decision-making robustness of the power grid.
Patent Information
- Application Number
- CN202510644985.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-20
- Publication Date
- 2026-03-03
- Estimated Expiration
- 2045-05-20
AI Technical Summary
Traditional line loss analysis methods cannot be accurate to specific nodes or regions, have poor real-time performance, ignore the influence of dynamic factors, have low calculation accuracy, and cannot capture the real-time changes of complex power grids, resulting in line loss calculation results deviating from reality.
By acquiring power line loss datasets, calculating Spearman rank correlation coefficients, conducting first-stage line loss constraint analysis and exponential smoothing residual analysis, and combining multi-stage constraint analysis, the superimposed effects of nonlinear factors such as line aging and load mutations are captured, thereby improving decision robustness.
It achieves real-time and accurate power line loss analysis, improves work efficiency, reduces manual workload, ensures the accuracy and reliability of analysis, and captures the impact of factors such as line aging and sudden load changes.
Smart Images

Figure CN120257211B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power line loss analysis technology, specifically to a power line loss analysis system and method based on big data. Background Technology
[0002] In power systems, line loss analysis is a crucial step in ensuring the economical operation of the power grid. However, traditional line loss analysis methods suffer from several limitations: insufficient data acquisition and processing; manual meter reading only provides overall line loss data, failing to pinpoint specific nodes or areas, and lacking real-time accuracy. For example, a regional power grid might discover a high overall line loss rate through manual meter reading, but it cannot quickly locate the specific high-loss line segment. Monitoring equipment methods are costly, have long deployment cycles, and limited coverage, making real-time monitoring of the entire network difficult. Traditional methods often rely on steady-state models or simplified formulas (such as the root mean square current method), neglecting the impact of dynamic factors (such as load fluctuations, equipment aging, and reactive power compensation status) on line losses. For instance, in distributed photovoltaic (PV) integration scenarios, traditional models struggle to accurately calculate line loss changes caused by bidirectional power flow. Furthermore, data from generation, transmission, and distribution are isolated, lacking a unified data sharing platform. For example, the lack of data communication between transformer maintenance teams and line maintenance teams leads to delays in fault handling, impacting line loss management efficiency. With the development of smart grids and information technology, the power industry has accumulated massive amounts of data, propelling line loss analysis into the big data era.
[0003] Chinese invention application CN119780536A discloses a power line loss analysis system and method for power transmission and transformation projects, including step one: acquiring real-time data, calculating real-time power line loss values based on the acquired data, and processing and analyzing the real-time power line loss values to determine whether the real-time power line loss values are abnormal; step two: acquiring real-time line temperature, deriving a relationship formula between line temperature and real-time power line loss values based on historical data of line temperature and real-time power line loss values, and plotting a temperature influence curve based on the relationship formula, thereby determining whether the real-time power line loss values are abnormal based on the temperature influence curve.
[0004] This allows for the development of corresponding measures and solutions; it can more accurately reflect the power line loss situation, improve the accuracy and efficiency of power line loss analysis; it helps reduce power line losses, thereby reducing energy waste and environmental pollution, promoting energy conservation, emission reduction and sustainable development, improving the power factor of the power system, and making the power system operate more efficiently and stably.
[0005] Chinese invention application CN119807965A discloses an intelligent analysis method for abnormal line loss in transformer substations, including the collection of basic data; the construction and training of an artificial intelligence line loss analysis model; anomaly detection and early warning; and adjustments and optimizations of power supply strategies by management personnel based on the pushed line loss analysis and detection results. This invention conducts in-depth analysis of line loss in transformer substations based on artificial intelligence technology, utilizes artificial intelligence to establish a line loss analysis model, and rapidly analyzes and locates line loss problems, thereby improving the efficiency of line loss analysis, reducing manual intervention and operational costs, and providing more accurate management and decision support for power supply management. It can reduce labor costs in power supply line loss management and improve work efficiency.
[0006] In the above invention applications, invention CN119780536A only considers the impact of temperature on line loss, but does not consider other influencing factors. Although invention CN119807965A considers other influencing factors, it relies on steady-state models or simplified formulas, ignoring the impact of dynamic factors on line loss. This makes it difficult to accurately calculate the changes in line loss caused by bidirectional power flow, resulting in line loss calculation results that deviate from reality, failing to capture the real-time changes of complex power grids, and having low calculation accuracy.
[0007] Therefore, the present invention provides a power line loss analysis system and method based on big data. Summary of the Invention
[0008] (a) Technical problems to be solved
[0009] To address the shortcomings of existing technologies, this invention provides a power line loss analysis system and method based on big data. This invention acquires a power line loss dataset, calculates the Spearman rank correlation coefficient between each power line loss data point and the line loss rate, outputs the strongly correlated factors of line loss for weighting, and performs a first line loss constraint analysis on the real-time data of the strongly correlated factors of each line to determine whether the constraints are met. If the first line loss constraint is not met, a second line loss constraint analysis command is sent out to perform exponential smoothing residual analysis on the strongly correlated factors of each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first and second constraint analysis results are combined to obtain a third constraint analysis result. The third constraint analysis result is used to render the line loss rate distribution in real time, further analyze the residuals, and capture the superimposed impact of nonlinear factors such as line aging and load abrupt changes on line loss. The first and second constraints are complementary; the former ensures basic accuracy, while the latter corrects for instantaneous fluctuations. Combining multi-stage constraint analysis improves decision robustness, thereby solving the technical problems described in the background art.
[0010] (II) Technical Solution
[0011] To achieve the above objectives, the present invention provides the following technical solution: 1. A power line loss analysis method based on big data, characterized by comprising the following steps:
[0012] Real-time collection of power grid equipment operating status and environmental parameters, aggregation of equipment ledgers, line parameters, geospatial data and user profiles, and the use of time series filtering algorithms to remove outliers to construct a power line loss dataset;
[0013] Acquire the power line loss dataset, calculate the Spearman rank correlation coefficient between each power line loss data and the line loss rate, output the strongly correlated factors of line loss and assign weights, perform the first line loss constraint analysis on the real-time data of the strongly correlated factors of line loss for each line, determine whether the constraint is met, and if the first line loss constraint is not met, send the second line loss constraint analysis command outward;
[0014] Upon receiving the second line loss constraint analysis command, the exponential smoothing residual method is used to analyze the line loss strongly correlated factors of each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result. The line loss rate distribution is rendered in real time based on the third constraint analysis result.
[0015] Furthermore, obtain the power line loss dataset and calculate the Spearman rank correlation coefficient between each power line loss data point and the line loss rate:
[0016] ;in, i Indicates the chronological sequence number of the sample data. i= 1, 2, 3, 4, ... n, n It is a positive integer. n This represents the total number of samples; and Sample data representing different power line loss data and line loss rates. and This represents the mean of the corresponding sample data.
[0017] Furthermore, power line loss data with a Spearman rank correlation coefficient greater than 0.5 are output as strongly correlated factors of line loss and weighted accordingly, specifically as follows:
[0018] ;in, Spearman rank correlation coefficient, representing factors strongly correlated with line loss.
[0019] Furthermore, the first constraint analysis specifically involves determining whether the real-time data of the line loss strongly correlated factors for each line are within the corresponding threshold. If they are within the threshold, they are recorded as 0; if they are not within the threshold, they are recorded as corresponding weights. All judgment results are summed and recorded as the first constraint analysis result. If the first constraint analysis result is greater than 0.1, it is considered that the line does not meet the first line loss constraint, and a second line loss constraint analysis command is sent out.
[0020] Furthermore, if the result of the first constraint analysis is not greater than 0.1, then the line is considered to meet the first line loss constraint. The result of the first constraint analysis is then output, and the line loss rate distribution is rendered in real time. Lines with a value greater than 0.1 and less than 0.5 are marked with orange rendering, and lines with a value greater than 0.5 are marked with red rendering.
[0021] Furthermore, upon receiving the second line loss constraint analysis command, the exponential smoothing residual method is used to analyze the strongly correlated factors of line loss for each line:
[0022] ; ; ;
[0023] Furthermore, the exponentially smoothed residuals of the line loss-related factors for each line are multiplied by the corresponding weights and then summed, which is denoted as the second constraint analysis result.
[0024] Furthermore, if the result of the second constraint analysis is not greater than 0.1, the result of the first constraint analysis is output, and the line loss rate distribution is rendered in real time. Lines with a loss rate greater than 0.1 but less than 0.5 are marked with orange rendering, and lines with a loss rate greater than 0.5 are marked with red rendering.
[0025] Furthermore, if the result of the second constraint analysis is greater than 0.1, then the results of the first and second constraint analyses are combined to obtain the result of the third constraint analysis. The line loss rate distribution is rendered in real time based on the result of the third constraint analysis. Lines with a loss rate greater than 0.1 but less than 0.5 are marked with orange, and lines with a loss rate greater than 0.5 are marked with red.
[0026] Furthermore, the result of the third constraint analysis is exp(second constraint analysis result * first constraint analysis result).
[0027] A power line loss analysis system based on big data includes:
[0028] The line loss data acquisition module collects the operating status and environmental parameters of power grid equipment in real time, aggregates equipment ledgers, line parameters, geospatial data and user profiles, and uses time series filtering algorithms to remove outliers to build a power line loss dataset.
[0029] The first line loss analysis module acquires the power line loss dataset, calculates the Spearman rank correlation coefficient between each power line loss data and the line loss rate, outputs the line loss strongly correlated factors for weighting, performs the first line loss constraint analysis on the real-time data of the line loss strongly correlated factors of each line, and determines whether the constraint is met. If the first line loss constraint is not met, the second line loss constraint analysis command is sent out.
[0030] After receiving the second line loss constraint analysis command, the second line loss analysis module performs exponential smoothing residual analysis on the line loss strongly correlated factors of each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result. The line loss rate distribution is rendered in real time based on the third constraint analysis result.
[0031] (III) Beneficial Effects
[0032] This invention provides a power line loss analysis system and method based on big data, which has the following beneficial effects:
[0033] 1. Real-time collection of power grid equipment operating status and environmental parameters, aggregation of equipment ledgers, line parameters, geospatial data and user profiles, and the use of time series filtering algorithms to remove outliers, constructing a power line loss dataset to provide real-time data support for power grid dispatching, equipment maintenance, etc., and help decision-makers make more reasonable decisions.
[0034] 2. Obtain the power line loss dataset, calculate the Spearman rank correlation coefficient between each power line loss data point and the line loss rate, output the strongly correlated factors of line loss for weighting, and perform a first line loss constraint analysis on the real-time data of the strongly correlated factors of each line to determine whether the constraints are met. If the first line loss constraint is not met, a second line loss constraint analysis command is sent out to provide basic data support for subsequent line loss analysis, ensuring the accuracy and reliability of the analysis. Through the application of big data technology, work efficiency is improved, manual workload is reduced, and problem-solving time is shortened.
[0035] 3. Upon receiving the second line loss constraint analysis command, the exponential smoothing residual method is used to analyze the strongly correlated factors of line loss for each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result. The line loss rate distribution is rendered in real time based on the third constraint analysis result, and the residual is further analyzed to capture the superimposed impact of nonlinear factors such as line aging and load changes on line loss. The first constraint and the second constraint are complementary. The former ensures basic accuracy, while the latter corrects instantaneous fluctuations. The combination of multi-stage constraint analysis improves decision robustness. Attached Figure Description
[0036] Figure 1This is a flowchart illustrating a power line loss analysis method based on big data according to the present invention.
[0037] Figure 2 This is a schematic diagram of the structure of a power line loss analysis system based on big data according to the present invention. Detailed Implementation
[0038] 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, and 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.
[0039] Please see Figure 1 This invention provides a power line loss analysis method based on big data, comprising the following steps:
[0040] Step 1: Collect real-time data on the operating status and environmental parameters of power grid equipment, aggregate equipment ledgers, line parameters, geospatial data and user profiles, and use time series filtering algorithms to remove outliers to construct a power line loss dataset.
[0041] Step one includes the following:
[0042] Step 101: Real-time acquisition of power grid equipment operating status and environmental parameters. Operating status includes current, voltage, power, three-phase imbalance, load rate, voltage deviation, harmonic content (THD), and line temperature, while environmental parameters include temperature and humidity.
[0043] Step 102: Aggregate equipment ledger, line parameters, and user files. The equipment ledger includes energy efficiency rating and metering equipment accuracy; the line parameters include length; and the user files include historical total load, historical maximum load, and historical average load.
[0044] Step 103: For 10kV distribution lines and high-loss transformer areas, collect key indicators such as power supply, power consumption of public / private transformers, power factor, and power supply radius.
[0045] Step 104: Use time series filtering algorithms to remove outliers caused by electricity theft and metering failures, and construct a power line loss dataset.
[0046] When using this method, refer to steps 101 to 104:
[0047] The system collects real-time data on the operating status and environmental parameters of power grid equipment, aggregates equipment ledgers, line parameters, geospatial data, and user profiles, and uses time series filtering algorithms to remove outliers to build a power line loss dataset. This provides real-time data support for power grid dispatching and equipment maintenance, helping decision-makers make more informed decisions.
[0048] Step 2: Obtain the power line loss dataset, calculate the Spearman rank correlation coefficient between each power line loss data and the line loss rate, output the strongly correlated factors of line loss and assign weights, perform the first line loss constraint analysis on the real-time data of the strongly correlated factors of line loss for each line, and determine whether the constraint is met. If the first line loss constraint is not met, send the second line loss constraint analysis command outward.
[0049] Step two includes the following:
[0050] Step 201: Obtain the power line loss dataset and calculate the Spearman rank correlation coefficient between each power line loss data point and the line loss rate.
[0051] ;in, i Indicates the chronological sequence number of the sample data. i= 1, 2, 3, 4, ... n, n It is a positive integer. n This represents the total number of samples; and Sample data representing different power line loss data and line loss rates. and This represents the mean of the corresponding sample data.
[0052] Step 202: Output power line loss data with Spearman rank correlation coefficients greater than 0.5 as strongly correlated factors of line loss, and assign weights accordingly. Specifically:
[0053] ;in, Spearman rank correlation coefficient, representing factors strongly correlated with line loss.
[0054] Step 203: Perform a first line loss constraint analysis on the real-time data of the line loss strongly correlated factors for each line to determine whether the constraints are met. If the first line loss constraint is not met, send a second line loss constraint analysis command outward.
[0055] The first constraint analysis specifically involves determining whether the real-time data of the line loss strongly correlated factors for each line are within the corresponding threshold. If they are within the threshold, they are recorded as 0; if they are not within the threshold, they are recorded as corresponding weights. All judgment results are summed and recorded as the first constraint analysis result. If the first constraint analysis result is greater than 0.1, it is considered that the line does not meet the first line loss constraint, and a second line loss constraint analysis command is sent out.
[0056] If the result of the first constraint analysis is not greater than 0.1, the line is considered to meet the first line loss constraint. The result of the first constraint analysis is then output, and the line loss rate distribution is rendered in real time. Lines with a value greater than 0.1 and less than 0.5 are marked with orange rendering, and lines with a value greater than 0.5 are marked with red rendering.
[0057] When using this method, refer to steps 201 to 203:
[0058] Acquire power line loss datasets, calculate the Spearman rank correlation coefficient between each power line loss data point and the line loss rate, output the strongly correlated factors of line loss for weighting, and perform a first line loss constraint analysis on the real-time data of the strongly correlated factors of each line to determine whether the constraints are met. If the first line loss constraint is not met, a second line loss constraint analysis command is sent out to provide basic data support for subsequent line loss analysis, ensuring the accuracy and reliability of the analysis. Through the application of big data technology, work efficiency is improved, manual workload is reduced, and problem-solving time is shortened.
[0059] Step 3: After receiving the second line loss constraint analysis command, perform exponential smoothing residual analysis on the line loss strongly correlated factors of each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, combine the first constraint analysis result and the second constraint analysis result to obtain the third constraint analysis result. Use the third constraint analysis result to render the line loss rate distribution in real time.
[0060] Step three includes the following:
[0061] Step 301: After receiving the second line loss constraint analysis command, perform exponential smoothing residual method analysis on the line loss strongly correlated factors for each line:
[0062] ; ; ;
[0063] The result of the second constraint analysis is obtained by multiplying the exponentially smoothed residuals of the factors strongly correlated with line loss for each line by the corresponding weights and summing them.
[0064] Step 302: If the result of the second constraint analysis is not greater than 0.1, output the result of the first constraint analysis and render the line loss rate distribution in real time. Lines with a loss rate greater than 0.1 and less than 0.5 are marked with orange rendering, and lines with a loss rate greater than 0.5 are marked with red rendering.
[0065] Step 303: If the result of the second constraint analysis is greater than 0.1, then the result of the first constraint analysis and the result of the second constraint analysis are combined to obtain the result of the third constraint analysis. The line loss rate distribution is rendered in real time based on the result of the third constraint analysis. Lines with a loss rate greater than 0.1 and less than 0.5 are marked with orange, and lines with a loss rate greater than 0.5 are marked with red.
[0066] The result of the third constraint analysis is exp(the result of the second constraint analysis) * the result of the first constraint analysis.
[0067] When using this method, refer to steps 301 to 303:
[0068] Upon receiving the second line loss constraint analysis command, the exponential smoothing residual method is used to analyze the strongly correlated factors of line loss for each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result. The line loss rate distribution is rendered in real time based on the third constraint analysis result, and the residual is further analyzed to capture the superimposed impact of nonlinear factors such as line aging and load changes on line loss. The first constraint and the second constraint are complementary. The former ensures basic accuracy, while the latter corrects instantaneous fluctuations. The combination of multi-stage constraint analysis improves decision robustness.
[0069] Please see Figure 2 This invention provides a power line loss analysis system based on big data, comprising:
[0070] The line loss data acquisition module collects the operating status and environmental parameters of power grid equipment in real time, aggregates equipment ledgers, line parameters, geospatial data and user profiles, and uses time series filtering algorithms to remove outliers to build a power line loss dataset.
[0071] The first line loss analysis module acquires the power line loss dataset, calculates the Spearman rank correlation coefficient between each power line loss data and the line loss rate, outputs the strongly correlated factors of line loss for weighting, performs the first line loss constraint analysis on the real-time data of the strongly correlated factors of line loss for each line, and determines whether the constraint is met. If the first line loss constraint is not met, the second line loss constraint analysis command is sent out.
[0072] After receiving the second line loss constraint analysis command, the second line loss analysis module performs exponential smoothing residual analysis on the line loss strongly correlated factors of each line to obtain the second constraint analysis result. If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result. The line loss rate distribution is rendered in real time based on the third constraint analysis result.
[0073] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.
[0074] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0075] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.
Claims
1. A big data-based power line loss analysis method, characterized in that: Comprising the following steps: Real-time acquisition of power grid equipment operating state and environmental parameters, aggregation of equipment account, line parameters, geographic spatial data and user archives, and adoption of time series filtering algorithm to eliminate abnormal values, to construct a power line loss dataset; Obtaining the power line loss dataset, calculating the Spearman rank correlation coefficient of each power line loss data and line loss rate, outputting the line loss strong correlation factors for weighting, performing first line loss constraint analysis on the real-time data of the line loss strong correlation factors of each line, and judging whether the constraint is met, if the first line loss constraint is not met, sending a second line loss constraint analysis command; The first constraint analysis is specifically to judge whether the real-time data of the line loss strong correlation factors of each line is within the corresponding threshold, if it is within the threshold, it is recorded as 0, if it is not within the threshold, it is recorded as the corresponding weight, and the sum of all judgment results is recorded as the first constraint analysis result, if the first constraint analysis result is greater than 0.1, it is considered that the line does not meet the first line loss constraint, and a second line loss constraint analysis command is sent out; After receiving the second line loss constraint analysis command, the line loss strong correlation factors of each line are analyzed by exponential smoothing residual method to obtain the second constraint analysis result, if the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result, and the third constraint analysis result is used for real-time rendering of line loss rate distribution; The exponential smoothing residual result of the line loss strong correlation factors of each line is multiplied by the corresponding weight and summed to obtain the second constraint analysis result.
2. The power line loss analysis method based on big data according to claim 1, characterized in that: If the first constraint analysis result is not greater than 0.1, it is considered that the line meets the first line loss constraint, and the first constraint analysis result is output for real-time rendering of line loss rate distribution, the line whose value is greater than 0.1 and less than 0.5 is marked with orange rendering, and the line whose value is greater than 0.5 is marked with red rendering.
3. The power line loss analysis method based on big data according to claim 1, characterized in that: If the second constraint analysis result is not greater than 0.1, the first constraint analysis result is output for real-time rendering of line loss rate distribution, the line whose value is greater than 0.1 and less than 0.5 is marked with orange rendering, and the line whose value is greater than 0.5 is marked with red rendering.
4. The power line loss analysis method based on big data according to claim 1, characterized in that: If the second constraint analysis result is greater than 0.1, the first constraint analysis result and the second constraint analysis result are combined to obtain the third constraint analysis result, and the third constraint analysis result is used for real-time rendering of line loss rate distribution, the line whose value is greater than 0.1 and less than 0.5 is marked with orange rendering, and the line whose value is greater than 0.5 is marked with red rendering.
5. The power line loss analysis method based on big data according to claim 1, characterized in that: The third constraint analysis result is exp(second constraint analysis result*first constraint analysis result).
6. A big data based power line loss analysis system for implementing the method of any one of claims 1 to 5, characterized in that: Comprising: The line loss data collection module collects the running state of the power grid equipment and environmental parameters in real time, gathers equipment account, line parameters, geographic space data and user archives, adopts a time series filtering algorithm to eliminate abnormal values, and constructs a power line loss data set; The line loss first analysis module obtains the power line loss data set, calculates the Spearman rank correlation coefficient of each power line loss data and line loss rate, outputs the line loss strong correlation factors for weighting, performs first line loss constraint analysis on the real-time data of the line loss strong correlation factors of each line, judges whether the constraint is satisfied, and if the first line loss constraint is not satisfied, sends a second line loss constraint analysis command; The line loss second analysis module receives the second line loss constraint analysis command, performs exponential smoothing residual method analysis on the line loss strong correlation factors of each line, obtains a second constraint analysis result, and if the second constraint analysis result is greater than 0.1, combines the first constraint analysis result and the second constraint analysis result to obtain a third constraint analysis result, and performs real-time rendering of the line loss rate distribution based on the third constraint analysis result.
Citation Information
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