A method for measuring similarity of user load curves based on piecewise linear approximation

Abstract

The present application relates to a new power system technology, in particular to a user load curve similarity measurement method based on piecewise linear approximation; by piecewise linear approximation to the user daily load curve electricity consumption data, the piecewise breakpoints of each two users are sorted in order, and the daily load curve is re-segmented; the slope, electricity consumption average and end time of each segment after re-segmentation are re-characterized; the difference between the slope and the total electricity consumption in different segments is calculated to evaluate the difference between the shape and the value of the daily load curve of different users; the weighted average of the shape difference and the value difference is calculated to calculate the total difference of the daily load curve; the total difference matrix of all users is constructed to calculate the daily load curve similarity between any two users; the present application overcomes the sensitivity of the existing user load curve similarity measurement method to extreme value and noise.

Description

Technical Field

[0001] This invention relates to a novel power system technology, specifically a method for measuring the similarity of user load curves based on piecewise linear approximation. Background Technology

[0002] The new power system has deployed a large number of smart meters, which periodically upload fine-grained electricity consumption data from users. The user load curves plotted based on this electricity consumption data accurately reflect users' electricity consumption habits. By measuring the similarity of users' load curves and further clustering them, the power grid company can better understand users' electricity consumption patterns, thereby formulating more reasonable operation and marketing strategies to ensure the safe, stable and efficient operation of the power system.

[0003] Measuring the similarity of user load curves is a crucial step in many power system applications. For example, in electricity theft detection, measuring the similarity of user load curves allows for grouping users with similar electricity consumption habits for monitoring, effectively improving the efficiency and accuracy of theft detection, reducing losses from electricity theft, and ensuring the safe and stable operation of the power system. In load forecasting, measuring the similarity of user load curves allows for the construction of federated learning-based load forecasting models for users with similar electricity consumption habits. This enables the prediction of user electricity consumption while protecting user privacy, helping power suppliers develop demand-driven marketing strategies and minimize operating costs.

[0004] Existing technologies for measuring the similarity of user load curves include Euclidean distance, Dynamic Time Warping (DTW), and symbolic distance aggregation approximation methods. Euclidean distance essentially measures the distance between vectors to determine similarity; closer distances indicate greater similarity. However, this geometric mean distance cannot adequately guarantee the similarity of curve shapes or contours and is highly susceptible to extreme values ​​and noise. DTW, on the other hand, uses dynamic programming to establish and calculate a two-dimensional cumulative cost matrix to obtain the minimum sum of distance values ​​between data points, using this as the distance value between sequences to measure curve similarity. However, this method has high time complexity and is difficult to apply to long time series or real-time scenarios. Symbolic distance aggregation approximation methods convert time series into strings of symbols, requiring similarity determination based on whether the trend symbols are the same. However, this method easily leads to the loss of other information in subsequence segments (such as trend information, variance information, and extreme value information), especially with higher data compression ratios, resulting in greater information loss. Summary of the Invention

[0005] The purpose of this invention is to address the problems of high computational complexity, low accuracy, and susceptibility to extreme values ​​in existing similarity measurement methods. This invention provides a user load curve similarity measurement method based on piecewise linear approximation. The method involves linearly approximating and segmenting the load curve, and then measuring the similarity of the segmented curves from both morphological and value similarity perspectives. This improves the accuracy and stability of the similarity measurement, while simplifying the similarity calculation method and increasing computational efficiency.

[0006] The technical solution of the present invention is as follows:

[0007] 1. A similarity measurement method for user load curves based on piecewise linear approximation, labeled for users ( ,and (Integer value) A smart meter is installed for each user, periodically uploading user electricity consumption data. (Tag) Tag the number of data uploaded by users each day. For users The smart meter on a certain day The electricity consumption data reported in each data reporting cycle, among which It is a positive integer. (Marked) user The time series of electricity consumption reported by a smart meter on a certain day. (Tag) For a given pair of users Daily load curve time series The number of segments.

[0008] Furthermore, it includes the following steps:

[0009] Step S1: For the user Daily load curve time series According to the given number of segments Perform piecewise linear approximation;

[0010] Step S2: For every two users , (in , and The daily load curve is segmented into linear approximate breakpoints, which are then sorted in chronological order, and the daily load curve is re-segmented to allow users to... and users The corresponding segment lengths are consistent;

[0011] Step S3: For every two users , (in , and The re-segmented daily load curve is re-characterized using three features: slope, average power consumption, and breakpoint time.

[0012] Step S4: Evaluate any two users by calculating the sum of the absolute values ​​of the differences between the slope and total electricity consumption in different segments. , The shape / numerical difference of the load curve; and through user and users The total load curve variance of a user is measured by a weighted average of the shape and numerical variance of the load curve.

[0013] Step S5: Through any two users , The total difference is used to construct a difference matrix for all users, and the similarity of daily load curves between any two users is calculated.

[0014] Further, step S1 includes:

[0015] Step S11: Mark Let be the set of breakpoints, where .mark and The first The slope and intercept of a linear approximation line segment, where ,and It is a positive integer.

[0016] Step S12: Mark For users The first of the daily load curves A set of approximate electricity consumption values ​​for each linear approximation line segment within a corresponding time period. (Marked) For users The first of the daily load curve A set of true power consumption values ​​for each linear approximation line segment within a corresponding time period.

[0017] Step S13: Minimize the deviation between the actual and approximate values ​​of power consumption (i.e., the set of values). With sets The set of linear approximation line segments is determined by the sum of the squares of the deviations between points in the equation. ,Right now .

[0018] Further, step S2 includes:

[0019] Step S21: Transfer the user and users The daily load curve obtained after step S1 is represented by the set of linear approximate line segments as follows: and The sets of their breakpoints are respectively represented as and ,in , .

[0020] Step S22: For and The breakpoints in the data are arranged in chronological order to obtain... ,in , ,and , where “=" is in the Obtained at that time.

[0021] Step S23: Transfer the user and users The load curve was recalculated based on The breakpoints in the middle are divided into Section, i.e. , .mark and users respectively The daily load curve after re-segmentation The slope and intercept of a linear approximation line segment, where ,and It is a positive integer. (Marked) .like Then there is Similarly, we can obtain .

[0022] Further, step S2 includes:

[0023] Step S21: Transfer the user and users The daily load curve obtained after step S1 is represented by the set of linear approximate line segments as follows: and The sets of their breakpoints are respectively represented as and ,in , .

[0024] Step S22: For and The breakpoints in the data are arranged in chronological order to obtain... ,in , ,and , where “=" is in the Obtained at that time.

[0025] Step S23: Transfer the user and users The load curve was recalculated based on The breakpoints in the middle are divided into Section, i.e. , .mark and users respectively The daily load curve after re-segmentation The slope and intercept of a linear approximation line segment, where ,and It is a positive integer. (Marked) .like Then there is Similarly, we can obtain .

[0026] Further, step S4 includes:

[0027] Step S41: Mark For users and users The degree of difference in the shape of the daily load curve. The calculation is as follows:

[0028] .

[0029] Step S42: Mark For users and users The numerical difference in the daily load curve. Then... The calculation is as follows:

[0030] .

[0031] Step S43: Mark For users and users The total variation of the daily load curve. Then The calculation is as follows:

[0032] ,

[0033] in For morphological differences sum of numerical differences The weighting factors between them.

[0034] Further, step S5 includes:

[0035] Step S51: Mark for The difference matrix of all users in the matrix, then the matrix The structure is as follows:

[0036]

[0037] Step S52: Mark and Each is a matrix The maximum and minimum values. (Marked) For users and users The similarity of their daily load curves. The calculation is as follows:

[0038] .

[0039] Compared with existing technologies, the advantages of this invention are:

[0040] A user load curve similarity measurement method based on piecewise linear approximation includes: Step S1: performing piecewise linear approximation on the load curve of each user; Step S2: sorting the segmentation breakpoints of every two users in chronological order and re-segmenting their daily load curves; Step S3: re-representing the daily load curves of every two users after re-segmentation; Step S4: calculating the morphological difference and numerical difference of the daily load curves of every two users after re-segmentation, and further calculating the total difference; Step S5: constructing the difference matrix of all users and calculating the similarity of the daily load curves between any two users. This method overcomes the sensitivity of existing user load curve similarity measurement methods to extreme values ​​and noise, and improves the accuracy, robustness, and computational efficiency of the algorithm. Attached Figure Description

[0041] Figure 1 A flowchart of a user load curve similarity measurement method based on piecewise linear approximation;

[0042] Figure 2 For users ,user and users Example plot of daily load time series;

[0043] Figure 3 For users ,user and users Example diagram of linear piecewise segmentation. Detailed Implementation

[0044] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0045] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0046] Example 1

[0047] Existing solutions for measuring the similarity of user load curves include: Euclidean distance, dynamic time warping (DTW), and symbol distance aggregation approximation methods, etc.

[0048] The essence of using Euclidean distance is to judge the degree of similarity by measuring the distance between vectors. The closer the distance, the more similar they are. However, the similarity of this geometric mean distance cannot fully guarantee the similarity of the shape or outline of the curve, and it is easily affected by extreme values ​​and noise.

[0049] DWT, on the other hand, uses dynamic programming to build and calculate a two-dimensional cumulative cost matrix to obtain the minimum sum of distance values ​​between data points, which is then used as the distance value between sequences to measure the similarity of curves. However, this method has a large time complexity and is difficult to use for time series with large lengths or in real-time scenarios.

[0050] The symbolic distance aggregation approximation method converts time series into a string of symbols, which requires determining similarity based on whether the trend symbols are the same. However, this method is prone to losing other information in the subsequence segments (such as trend information, variance information, extreme value information, etc.), especially when the data compression ratio is higher, more information will be lost.

[0051] To address the aforementioned issues, this embodiment proposes a user load curve similarity measurement method based on piecewise linear approximation. By acquiring time-series load curves of different users over a period of time, a piecewise linear approximation is performed on the load curve of each user. The user load curves are then re-represented to evaluate the morphological and value differences of the load curves. A formula for measuring the overall similarity of the curves is constructed by combining these two differences, reducing the sensitivity of the load curves to extreme values ​​and noise, making the algorithm more stable, improving the accuracy of curve similarity measurement, and increasing computational efficiency.

[0052] Please see Figure 1 A user load curve similarity measurement method based on piecewise linear approximation, specifically including the following steps:

[0053] Step S1: As Figure 2 As shown, assume there are a total of 3 users. The smart meter's data reporting cycle is 15 minutes, meaning the smart meter uploads a certain number of data points per day. Obtain the daily load curve time series for three users respectively. {35.52,31.97,24.87,21.31,15.99,15.99,21.31,23.09,26.64,39.08,51.51,55.06,39.08,39.08,37.3,60.39,83.48,81.71,72.82,63.94,71.05,60.39,60.39,63. 94,69.27,69.27,71.05,62.17,60.39,65.72,63.94,55.06,44.4,49.73,49.73,53.29,49.73,44.4,55.06,53.29,60.39,60.39,51.51,49.73,55.06,55.06,56.84,55. 06,53.29,47.96,47.96,46.18,46.18,56.84,42.63,42.63,39.08,44.4,44.4,47.96,55.06,58.61,56.84,60.39,58.61,62.17,67.5,74.6,81.71,78.15,78.15,67.5, 60.39,53.29,56.84,53.29,46.18,46.18,44.4,49.73,46.18,49.73,47.96,46.18,35.52,40.85,33.75,33.75,28.42,30.2,31.97,33.75,30.2,33.75,28.42,31.97}; {35.25,36.43,39.95,37.6,30.55,28.2,28.2,29.38,42.3,47,51.7,62.28,74.03,66.98,76.38,71.68,66.98,69.33,58.75,59.93,59.93,59.93,52.88,51.7,45.83,37.6,43.48,48.18,48.18,47,41.13,37.6,39.95,41.13,42.3,39.95,35.25,37.6,42.3,39.95,38.78,38.78,41.13,39.95,43.48,42.3,43.48,44.65,43.48,42.3,42.3,39.95,43.48,42.3,43.48,50.53,62.28,70.51,77.56,88.13,91.66,102.23,101.06,96.36,91.66,89.31,91.66,96.36,88.13,81.08,79.91,81.08,76.38,81.08,71.68,72.86,69.33,58.75,49.35,49.35,54.05,56.4,45.83,44.65,42.3,42.3,43.48,41.13,37.6,38.78,41.13,37.6,35.25,37.6,35.25,39.95}; {25.86,26.55,27.25,25.16,24.46,23.06,23.06,21.66,25.16,27.95,31.45,35.64,31.45,34.24,34.24,31.45,37.04,39.83,37.04,36.34,36.34,35.64,35.64,37.74 ,41.23,46.12,41.93,39.13,39.13,39.83,44.72,48.92,41.23,37.04,34.94,32.84,36.34,34.94,40.53,36.34,36.34,37.74,38.43,40.53,41.23,34.24,36.34,34.24, 37.04, 37.74, 35.64, 34.94, 34.94, 39.13, 39.13, 40.53, 43.33, 50.31, 48.22, 48.92, 51.71, 49.62, 47.52, 43.33, 39.13, 40.53, 46.12, 44.72, 44.72, 45.42, 41.93, 38.43, The daily load curve time series of the above three users are all piecewise linearly approximated according to a given number of segments of 7, i.e. .

[0054] Step S2: For the user set Every two users , (in , and The daily load curve is segmented into linear approximate breakpoints, which are then sorted in chronological order, and the daily load curve is re-segmented to allow users to... and users The corresponding segment lengths are consistent;

[0055] Step S3: For every two users , (in , and The re-segmented daily load curve is re-characterized using three features: slope, average electricity consumption, and the end time of the segment.

[0056] Step S4: Evaluate any two users by calculating the sum of the absolute values ​​of the differences between the slope and total electricity consumption in different segments. , The shape / numerical difference of the load curve; and through user and users The total load curve variance of a user is measured by a weighted average of the shape and numerical variance of the load curve.

[0057] Step S5: Through any two users , The total difference is used to construct a difference matrix for all users, and the similarity of daily load curves between any two users is calculated.

[0058] In this embodiment, specifically, step S1 includes:

[0059] Step S11: Perform linear segmentation according to the given number of 7 segments, and process the data for the user. , and thus , , , , , , For users , and thus , , , , , , For users , and thus , , , , , , .

[0060] In this embodiment, specifically, step S2 includes:

[0061] Step S21: For the user and users The sets of linear approximate line segments obtained after step S1 are, i.e. , Their breakpoint sets are respectively {1, 5, 15, 17, 58,71, 74, 96} {1, 7, 14, 26, 55, 62, 85, 96}. Similarly, we can deduce that the user... breakpoint set {1, 32, 35, 43, 53, 60, 84, 96}.

[0062] Step S22: For the user and users Set of breakpoints after linear segmentation and Arranged in chronological order, we get {1, 5, 7, 14, 15, 17, 26, 55, 58, 62, 71, 74, 85, 96}. Similarly, we can obtain... {1, 5, 15, 17, 32, 35, 43, 53, 58, 60, 71, 74, 84, 96}, and {1, 7,14, 26, 32, 35, 43, 53, 55, 60, 62, 84, 85, 96}.

[0063] Step S23: According to Breakpoints in the code will allow users to... and users Reorganized into 13 segments for users ,according to , and thus Similarly, we can conclude that... , , , , , , , , , , , For users , and thus , , , , , , , , , , , , .

[0064] In this embodiment, specifically, step S3 includes:

[0065] Step S31: According to After the breakpoint is re-segmented, the user is calculated. and users Average power consumption within each segment. For users. , and thus , , , , , , , , , , , , For users , and thus , , , , , , , , , , , , .

[0066] Step S32: For the user The first of its daily load curve A linear approximation line segment is obtained by using the slope of that segment. Average power consumption Breakpoint time That is, triplet Then, it is re-characterized. The breakpoint in the middle, then the user Daily load curve time series This can be re-characterized as {(-4.97, 25.93, 5),(3.10, 18.65, 7),(3.10, 39.08, 14),(3.10, 37.30, 15),(15.60, 71.94, 17),(-0.69, 68.09, 26),(-0.69, 53.90, 55),(-0.69, 42.04, 58),(2.97, 51.51,62),(2.97, 68.68, 71),(-8.87, 60.39, 74),(-1.22, 47.47, 85),(-1.22,32.46, 96)}; User Daily load curve time series It can be recharacterized as {(-1.67, 35.96, 5), (-1.67, 28.20, 7), (6.84, 53.38, 14), (-2.95, 76.38, 15), (-2.95, 69.33, 17), (-2.95, 55.10, 26), (-0.04, 41.86, 55), (8.35, 61.11, 58), (8.35, 89.90, 62), (-2.62, 90.61, 71), (-2.62, 79.51, 74), (-2.62, 55.87, 85), (-0.56, 39.10,96)}.

[0067] Similarly, according to The breakpoint in the middle, then the user Daily load curve time series This can be recharacterized as {(-4.97, 25.93, 5), (3.10, 34.81, 15), (15.60, 71.94, 17), (-0.69, 66.07,32), (-0.69, 47.95, 35), (-0.69, 53.51, 43), (-0.69, 51.33, 53), (-0.69,45.12, 58), (2.97, 46.18, 60), (2.97, 66.53, 71), (-8.87, 60.39, 74), (-1.22,48.67, 84), (-1.22, 32.71, 96)}; User Daily load curve time series It can be recharacterized as {(0.71, 25.86, 5), (0.71, 28.79,15), (0.71, 34.25, 17), (0.71, 39.97, 32), (-4.18, 37.74, 35), (0.50, 36.69, 43), (-0.52, 36.69, 53), (2.37, 42.49, 58), (2.37, 48.57, 60), (-1.05, 44.98, 71), (-1.05, 38.20, 74), (-1.05, 29.63,84), (0.00, 25.04, 96)}.

[0068] according to The breakpoint in the middle, then the user Daily load curve time series This can be recharacterized as {(-1.67,33.74, 7), (6.84, 53.38, 14), (-2.95, 59.24, 26), (-0.04, 44.26, 32), (-0.04,41.13, 35), (-0.04, 39.22, 43), (-0.04, 42.54, 53), (-0.04, 42.89, 55),(8.35, 69.80, 60), (8.35, 96.95, 62), (-2.62, 73.92, 84), (-2.62, 42.30, 85),(-0.56, 39.10, 96)}; User Daily load curve time series It can be recharacterized as {(0.71, 25.06,7), (0.71, 29.65, 14), (0.71, 37.39, 26), (0.71, 42.28, 32), (-4.18, 37.74,35), (0.50, 36.69, 43), (-0.52, 36.69, 53), (2.37, 39.13, 55), (2.37, 46.26,60), (-1.05, 50.67, 62), (-1.05, 36.56, 84), (0.00, 25.16, 85), (0.00, 25.03,96)}.

[0069] In this embodiment, specifically, step S4 includes:

[0070] Step S41: Based on the data re-characterized in step S32, it can be concluded that the user... and users Difference in the shape of daily load curves ;user and users Difference in the shape of daily load curves ;user and users Difference in the shape of daily load curves .

[0071] Step S42: Based on the data re-represented in step S32, it can be concluded that the user... and users Daily load curve numerical difference ;user and users Daily load curve numerical difference ;user and users Daily load curve numerical difference .

[0072] Step S43: Assume Based on the morphological and numerical differences calculated in steps S41 and S42, it can be concluded that the user and users Total variability of daily load curves ;user and users Total variability of daily load curves ;user and users Total variability of daily load curves .

[0073] In this embodiment, specifically, step S5 includes:

[0074] Step S51: Based on the total difference value calculated in step 43, construct the user... ,user and users From the difference matrix, we can derive:

[0075]

[0076] Step S52: Based on the difference matrix of all users in step 51 By calculating the similarity of the daily load curves for every two users, it can be concluded that the users and users Daily load curve similarity ;user and users Daily load curve similarity ;user and users Daily load curve similarity .

[0077] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

[0078] This background section is provided to generally present the context of the invention. The work of the currently named inventors, the work to the extent described in this background section, and aspects of this section that did not constitute prior art at the time of application are neither expressly nor impliedly acknowledged as prior art to the invention.

Claims

1. A method for measuring the similarity of user load curves based on piecewise linear approximation, characterized in that, mark for There are 10 users, of which: ,and The value is an integer; a smart meter is installed for each user, and user electricity consumption data is uploaded periodically; [The following is a list of tags / markers] Tag the number of data uploaded by users each day. For users The smart meter on a certain day The electricity consumption data reported in each data reporting cycle, among which A positive integer; marked user The time series of electricity consumption reported by the smart meter on a certain day; marked For a given pair of users Daily load curve time series The number of segments; Includes the following steps: Step S1: For the user Daily load curve time series According to the given number of segments Perform piecewise linear approximation; Step S2: For every two users , The daily load curve is segmented into linear approximate breakpoints and ordered sequentially. The daily load curve is then re-segmented to allow users to... and users The corresponding segment lengths are consistent, where: , and ; Step S3: For every two users , The re-segmented daily load curve is re-characterized for each segment using three features: slope, average electricity consumption, and the end time of that segment. , and ; Step S4: Evaluate any two users by calculating the sum of the absolute values ​​of the differences between the slope and total electricity consumption across all segments. , The shape / numerical difference of the load curve; and through user and users The total load curve variance of a user is measured by a weighted average of the morphological and numerical variances of the load curves. Step S5: Through any two users , The total difference is used to construct a difference matrix for all users, and the similarity of daily load curves between any two users is calculated.

2. The user load curve similarity measurement method based on piecewise linear approximation according to claim 1, characterized in that, Step S1 includes: Step S11: Mark Let be the set of breakpoints, where ;mark and The first The slope and intercept of a linear approximation line segment, where ,and It is a positive integer; Step S12: Mark For users The first of the daily load curve A set of approximate power consumption values ​​for each linear approximation segment within a corresponding time period; (marked) For users The first of the daily load curve A set of actual power consumption values ​​for each linear approximation line segment within the corresponding time period; Step S13: Determine the set of linear approximation line segments by minimizing the sum of squares of the deviations between the true and approximate values ​​of power consumption. ,Right now .

3. The user load curve similarity measurement method based on piecewise linear approximation according to claim 2, characterized in that, Step S2 includes: Step S21: Transfer the user and users The daily load curve obtained after step S1 is represented by the set of linear approximate line segments as follows: and The sets of their breakpoints are respectively represented as and ,in , ; Step S22: For and The breakpoints in the data are arranged in chronological order to obtain... ,in , ,and , where "=" is in the Obtained in time; Step S23: Transfer the user and users The load curve was recalculated based on The breakpoints in the middle are divided into Section, i.e. , ;mark and users respectively The daily load curve after re-segmentation The slope and intercept of a linear approximation line segment, where ,and A positive integer; marked ;like Then there is Similarly, we can obtain .

4. The user load curve similarity measurement method based on piecewise linear approximation according to claim 3, characterized in that, Step S3 includes: Step S31: Mark For users During the data reporting cycle and Average power consumption within the range; calculation Similarly, we can obtain ; Step S32: For the user The first of its daily load curve A linear approximation line segment is obtained by using the slope of that segment. Average power consumption and the end time of this segment That is, triplet Then, the user will be re-represented; Daily load curve time series It can be recharacterized as Similarly, the user Daily load curve time series It can be recharacterized as .

5. The user load curve similarity measurement method based on piecewise linear approximation according to claim 4, characterized in that, Step S4 includes: Step S41: Mark For users and users The degree of difference in the shape of the daily load curve, then The calculation is as follows: ； Step S42: Mark For users and users The numerical difference in the daily load curve, then The calculation is as follows: ； Step S43: Mark For users and users The total variability of the daily load curve, then The calculation is as follows: ； in: For morphological differences sum of numerical differences The weighting factors between them.

6. The user load curve similarity measurement method based on piecewise linear approximation according to claim 5, characterized in that, Step S5 includes: Step S51: Mark for The difference matrix of all users in the matrix, then the matrix The structure is as follows: ； Step S52: Mark and Each is a matrix Maximum and minimum values; marking For users and users The similarity of their daily load curves; then The calculation is as follows: 。

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