Power system load fluctuation section data compression method based on compressed sensing

Abstract

The invention relates to an electric power system load fluctuation section data compression method based on compressed sensing, which is characterized by comprising the following steps of: 1, dividing an event section and a non-event section based on available load power consumption data; 2, dividing a non-event section into a fluctuation section and a stationary section; 3, performing compression processing on the fluctuation segment data extracted in the step 2 by adopting a compressed sensing-based data compression and reconstruction method; 4, reconstructing the original data of the fluctuation section data by adopting an optimized SAMP method; and 5, evaluating the reconstruction precision by taking the RMSE and the MPPE as evaluation indexes. According to the method, the data compression efficiency can be further improved while certain data reconstruction precision is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of data compression of advanced measurement systems, and relates to a fluctuation segment data compression method, in particular to a power system load fluctuation segment data compression method based on compressed sensing. Background Art

[0002] Electricity is an important secondary energy form and plays a vital role in the development of modern economy and society. At present, with the development of economy and the improvement of living standards, the demand for industrial electricity and the electricity consumption of residents have increased significantly. The power industry has become a basic industry and an important public utility to support the development of national economy. However, with the challenges of resource shortage, environmental pollution, greenhouse effect and so on, the development of smart grid has become an inevitable choice. The emergence and popularization of advanced measurement system has played an important role in improving the measurement and transmission of information, which is convenient for the full analysis and application of user electricity information, making it possible to analyze and identify user electricity behavior, predict load, and respond to power system demand, improve the technical capacity of public service for safe electricity use, tap the load regulation capacity, improve the level of energy service, reduce energy waste, and respond to corresponding challenges and crises.

[0003] However, large amounts of data transmission and storage have brought tremendous pressure to the realization of communication equipment and functional requirements. Conducting relevant research on data compression to save data storage capacity and reduce data communication bandwidth as much as possible while retaining useful information has become an urgent problem to be solved.

[0004] Existing data compression methods are mainly divided into lossy compression and lossless compression.

[0005] The so-called lossless compression is to achieve the purpose of data compression by removing some redundant information in the original representation information and reducing the redundancy in the information. This method can retain all the information of the original data, but the compression ratio is lower than that of lossy compression.

[0006] Lossy compression allows the original information to be lost within a certain range. It achieves the purpose of data compression by identifying unnecessary information in the data and removing it. In the fields of image, video, industry and medicine, there are special compression methods designed for the data characteristics of different fields. There are many studies on lossy compression methods. There are some data compression methods based on piecewise function approximation. By dividing the time series according to certain rules, each segment is approximated by a corresponding function to compress the data; the existing compressed sensing technology can also compress and reconstruct the signal at a rate far lower than the rate required by the Nyquist sampling theorem, and has good applications in many fields such as image processing and biomedicine; there are also some lossy compression methods that use singular value decomposition technology to reduce the amount of data, and reconstruct the data transmitted by it using matrix multiplication, so as to achieve the effect of data compression while retaining the amount of information.

[0007] However, the power load data itself contains a large amount of information. How to compress the power load data according to the characteristics of the power system load data while minimizing the loss of its inherent characteristic information and forming an effective compression method suitable for the power system load data is a technical problem that needs to be solved urgently by ordinary technicians in this field.

[0008] After searching, no public documents of the prior art that are identical or similar to the present invention were found. Summary of the invention

[0009] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a data compression method for load fluctuation segments of power systems based on compressed sensing. In order to further improve the efficiency of data compression while ensuring a certain data reconstruction accuracy, based on event detection and compressed sensing theory, key information is retained as much as possible, and data compression is performed at the same time, the transmission communication bandwidth is reduced, the communication pressure is alleviated, and a good compression effect is obtained.

[0010] The present invention solves the practical problem by adopting the following technical solutions:

[0011] A method for compressing data of load fluctuation segments of a power system based on compressed sensing comprises the following steps:

[0012] Step 1: Based on the available load power consumption data, event monitoring is performed through edge detection algorithm to divide the event segment into the event segment and the non-event segment;

[0013] Step 2, extract the non-event segment after the division in step 1, and further divide it, use the fluctuation detection algorithm to further detect the fluctuation segment data, and then divide the non-event segment into a fluctuation segment and a stable segment;

[0014] Step 3: compress the fluctuation segment data extracted in step 2 by using a data compression and reconstruction method based on compressed sensing;

[0015] Step 4: for the compressed fluctuation segment data obtained in step 3, the original data of the fluctuation segment data is reconstructed by using the optimized SAMP method;

[0016] Step 5: Use RMSE and MPPE as evaluation indicators to evaluate the reconstruction accuracy.

[0017] Moreover, the specific method of step 2 is:

[0018] The voltage effective value detection method is used to extract the power system fluctuation segment data, and the remaining part of the non-event segment is the stable segment. The effective value of the voltage signal in the sliding window is calculated and compared with the preset threshold to detect the part corresponding to the fluctuation segment and extract the fluctuation segment:

[0019] Determine the time length of the sliding window. The reference value is 0.5s-4s. The window length can be adjusted according to the specific data characteristics.

[0020] For each sliding window, calculate the effective voltage value of the voltage signal within the window:

[0021]

[0022] Where x is the voltage value of the kth sampling point in the window; N is the number of sampling points in the window.

[0023] The threshold is set based on statistical characteristics or experience, and the threshold is set to the voltage effective value plus the standard deviation:

[0024] V=μ+ασ

[0025] Among them, μ is the mean value, σ is the standard deviation, and α is usually 1 or 2, which can be adjusted according to actual needs;

[0026] For each sliding window, it is judged whether its effective value exceeds the threshold. If the effective values ​​of multiple consecutive windows exceed the threshold, they are merged into a fluctuation segment, and the corresponding start time and end time are recorded. The fluctuation segment is extracted, and the remaining part is the stable segment, thereby realizing the division of non-event segments into fluctuation segments and stable segment data.

[0027] Moreover, in the step 3, in terms of sparse basis optimization, a redundant dictionary MOD method is used to optimize the sparse basis, and a Gaussian matrix is ​​used as a measurement matrix;

[0028] The specific steps include:

[0029] (1) Initialization: setting the initial dictionary Ψ0 = Ψ, extracting characteristic signals from the power operation equipment, performing vector normalization, and generating the initial dictionary;

[0030] (2) Input the training set and the number of dictionary atoms into the system. The training set is the original signal collected from the power system. The number of dictionary atoms should be greater than the dimension of the original signal itself so that there is sufficient expression ability to perform diversified representation of the power signal.

[0031] (3) Perform learning iterations, and iterate the information input into the system under the following constraints:

[0032]

[0033] (4) After the iteration, At this point, learning is stopped, and the obtained dictionary and the corresponding sparse coefficient matrix are output to obtain a compressed representation of the fluctuation segment data after compression processing.

[0034] Moreover, the specific steps of step 4 include:

[0035] a) Input: The following parameters are used: number of iterations t = 1; residual r0 = y, which is the low-dimensional representation of the compressed power load data; matching matrix A = ΦΨ (A∈R M×N ); step sequence s; variable initialization i=1; index set ; Initial step length L = γ t ; Adjustment factor γ = linspace(F,E,D), where F = arctan(s) × M / 4π; E = s; D = M / 4;

[0036] b) Discrimination: residual calculation u t = {u t |u t =| <r t-1 ,a t >|,1≤j≤N}, take out the column number set S k ={j|max(u j ,L)}, find the column number with the largest correlation with the residual;

[0037] c) Atom candidate set update: add the column number set selected in the current iteration to the index set of the previous round to generate a new atom candidate set: t =Λ t-1 ∪S k , A t =a j ,j∈C k ; Update the estimated value of the signal sparse representation coefficient:

[0038] d) Update the support set: Let A tk Use the corresponding A t The K columns in are represented by Λ tk Representation; residual update:

[0039] e) Update the number of iterations and determine whether to terminate. If ||r t ||2→0, stop iteration and go to step h); otherwise, execute the next step;

[0040] f) If || r t ||2<||r t-1 ||2, and L<N, then update the step size, L=L+γ t , γ=linspace(F,E,D)t=t+1, return to step b);

[0041] g) If || r t ||2>||r t-1 ||2, and L<N, then update the step size, t=t+1, return to step b); otherwise, go to step h);

[0042] h) Estimation Set Λ t Put non-zero items in Store the iteration value in and reconstruct the signal That is, the reconstructed fluctuation segment data is obtained.

[0043] Moreover, the reconstruction accuracy evaluation index formula of step 5 is:

[0044]

[0045]

[0046] Where T represents the time length corresponding to the data used; M i Indicates the size of the original data value at time i; M i ′ represents the size of the reconstructed data value at the corresponding time i; peak represents the daily peak data size.

[0047] Advantages and beneficial effects of the present invention:

[0048] 1. Aiming at the problem that a large amount of data transmission and storage nowadays has brought tremendous pressure to the realization of communication equipment and functional requirements, the present invention proposes a data compression method for load fluctuation segment of power system based on compressed sensing. The original load data is divided into event segment, fluctuation segment and stable segment by using event detection method and fluctuation detection method. For the fluctuation segment data, the fluctuation is relatively obvious and the information density is relatively large. The data compression and reconstruction method based on compressed sensing is adopted, so that the data compression can reduce the communication bandwidth and alleviate the communication pressure while retaining more key information, and has a better compression effect.

[0049] 2. The present invention proposes a method for compressing data in the load fluctuation segment of a power system based on compressed sensing. For the acquired data, different data segments are divided according to the different characteristics of the information data contained therein. For the fluctuation segment data, the unit information content is relatively large and the information is relatively rich. The compressed sensing theory is used to perform relevant compression processing, data compression, storage and transmission, and finally data reconstruction. This method can reduce the communication bandwidth as much as possible while storing key information and improve compression efficiency.

[0050] 3. Based on event detection and fluctuation detection methods, the present invention divides data into event segments, fluctuation segments and stable segments. For the fluctuation segments extracted, the unit information content is relatively large and the information is relatively rich. The compressed sensing theory is used to perform relevant compression processing, data compression, storage and transmission, and finally data reconstruction. This method can reduce the communication bandwidth as much as possible while storing key information and improve compression efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the fluctuation segment data compression method based on compressed sensing of the present invention. DETAILED DESCRIPTION

[0052] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings:

[0053] A data compression method for load fluctuation segment of power system based on compressed sensing, such as Figure 1 As shown, the following steps are included:

[0054] Step 1: Based on the available load power consumption data, event monitoring is performed through edge detection algorithm to divide the event segment into the event segment and the non-event segment;

[0055] The meanings of the segments represented by the event segment and the non-event segment in step 1 are:

[0056] The event segment refers to the process of the change of the operating state of the electrical equipment, including the switching operation of the electrical equipment and the switching between different operating state modes.

[0057] In this embodiment, this process is manifested in terms of power as a change in power value, whose waveform is relatively complex and contains rich and useful information, providing a basis for relevant data analysis and application;

[0058] The non-event segment refers to the data segment between two event segments, and its operating state remains stable without obvious power value fluctuations.

[0059] In this embodiment, when data compression is performed on this section, an efficient compression effect can be achieved;

[0060] Step 2, extract the non-event segment after the division in step 1, and further divide it, use the fluctuation detection algorithm to further detect the fluctuation segment data, and then divide the non-event segment into a fluctuation segment and a stable segment;

[0061] The specific method of step 2 is:

[0062] The voltage effective value detection method is used to extract the power system fluctuation segment data, and the remaining part of the non-event segment is the stable segment. The effective value of the voltage signal in the sliding window is calculated and compared with the preset threshold to detect the part corresponding to the fluctuation segment and extract the fluctuation segment:

[0063] Determine the time length of the sliding window. The reference value is 0.5s-4s. The window length can be adjusted according to the specific data characteristics.

[0064] For each sliding window, calculate the effective voltage value of the voltage signal within the window:

[0065]

[0066] Where x is the voltage value of the kth sampling point in the window; N is the number of sampling points in the window.

[0067] The threshold is set based on statistical characteristics or experience, and the threshold is set to the voltage effective value plus the standard deviation:

[0068] V=μ+ασ

[0069] Among them, μ is the mean value, σ is the standard deviation, and α is usually 1 or 2, which can be adjusted according to actual needs.

[0070] For each sliding window, it is judged whether its effective value exceeds the threshold. If the effective values ​​of multiple consecutive windows exceed the threshold, they are merged into a fluctuation segment, and the corresponding start time and end time are recorded. The fluctuation segment is extracted, and the remaining part is the stable segment, thereby realizing the division of non-event segments into fluctuation segments and stable segment data.

[0071] Step 3: compress the fluctuation segment data extracted in step 2 by using a data compression and reconstruction method based on compressed sensing;

[0072] In the step 3, in terms of sparse basis optimization, a redundant dictionary MOD method is used to optimize the sparse basis, and a Gaussian matrix is ​​used as a measurement matrix;

[0073] The specific steps include:

[0074] (1) Initialization: setting the initial dictionary Ψ0 = Ψ, extracting characteristic signals from the power operation equipment, performing vector normalization, and generating the initial dictionary;

[0075] (2) Input the training set and the number of dictionary atoms into the system. The training set is the original signal collected from the power system. The number of dictionary atoms should be greater than the dimension of the original signal itself so that there is sufficient expression ability to perform diversified representation of the power signal.

[0076] (3) Perform learning iterations, and iterate the information input into the system under the following constraints:

[0077]

[0078] (4) After the iteration, At this point, learning is stopped, and the obtained dictionary and the corresponding sparse coefficient matrix are output to obtain a compressed representation of the fluctuation segment data after compression processing.

[0079] In this embodiment, the working principle of step 3 is:

[0080] Compressed sensing, also known as compressed sampling, can acquire discrete samples of signals at a sampling rate much lower than Nyquist, and reconstruct the signals under the coordination of corresponding algorithms.

[0081] Basic theory of compressed sensing:

[0082] The core idea of ​​compressed sensing is that many natural signals and data are inherently sparse or can be sparsely represented, that is, the coefficients of the signal in a certain representation are mostly zero. This means that we do not need to fully sample all parts of the signal, but only need to collect a relatively small part of the effective information, so that we can efficiently collect effective information, while reducing the sampling points and the amount of information transmitted.

[0083] Compressed sensing has three important parts, namely, sparse basis, measurement matrix and reconstruction method. The optimization of these three parts has a great influence on the overall effect of compressed sensing. In terms of sparse basis optimization, the present invention adopts the redundant dictionary MOD method to optimize the sparse basis and adopts the Gaussian matrix as the measurement matrix.

[0084] Sparse Basis Optimization for Compressed Sensing:

[0085] The processing object of compressed sensing needs to be sparse. In order to ensure the sparsity of the processed information, the redundant dictionary MOD method is first used. The MOD learning method uses an iterative alternating update method to update the dictionary atoms, so that the dictionary with the smallest residual value can be found while making the sparse coefficient as small as possible, and the data is sparsely represented:

[0086] (1) Initialization: setting the initial dictionary Ψ0 = Ψ, extracting characteristic signals from the power operation equipment, performing vector normalization, and generating the initial dictionary;

[0087] (2) Input the training set and the number of dictionary atoms into the system. The training set is the original signal collected from the power system. The number of dictionary atoms should be greater than the dimension of the original signal itself so that there is sufficient expression ability to perform diversified representation of the power signal.

[0088] (3) Perform learning iterations, and iterate the information input into the system under the following constraints:

[0089]

[0090] (4) After the iteration, At this point, learning is stopped, and the obtained dictionary and the corresponding sparse coefficient matrix are output to obtain a compressed representation of the fluctuation segment data after compression processing.

[0091] Compression degree CR calculation formula:

[0092]

[0093] Among them, S0 represents the amount of data before compression; S represents the amount of data required for data transmission, storage, etc. after compression.

[0094] Step 4: for the compressed fluctuation segment data obtained in step 3, the original data of the fluctuation segment data is reconstructed by using the optimized SAMP method;

[0095] The specific steps of step 4 include:

[0096] a Input: Use the following parameters: number of iterations t = 1; residual r0 = y, which is the low-dimensional representation of the compressed power load data; matching matrix A = ΦΨ (A∈R M×N ); step sequence s; variable initialization i=1; index set Initial step length L = γ t; Adjustment factor γ = linspace(F,E,D), where F = arctan(s) × M / 4π; E = s; D = M / 4;

[0097] b judgment: residual calculation u t = {u t |u t =| <r t-1 ,a t >|,1≤j≤N}, take out the column number set S k ={j|max(u j ,L)}, find the column number with the largest correlation with the residual;

[0098] c atomic candidate set is updated, the column sequence number set selected in the current iteration is added to the index set of the previous round to generate a new atomic candidate set: t =Λ t-1 ∪S k , A t =a j ,j∈C k ; Update the estimated value of the signal sparse representation coefficient:

[0099] d Update the support set: Let A tk Use the corresponding A t The K columns in are represented by Λ tk Representation; residual update:

[0100] e updates the number of iterations and determines whether to terminate. If ||r t ||2→0, stop iteration and go to step h); otherwise, execute the next step;

[0101] f if || r t ||2<||r t-1 ||2, and L<N, then update the step size, L=L+γ t , γ=linspace(F,E,D)t=t+1, return to step b);

[0102] gIf||r t ||2>||r t-1 ||2, and L<N, then update the step size, t=t+1, return to step b); otherwise, go to step h);

[0103] h estimate : Set Λ t Put non-zero items in Store the iteration value in and reconstruct the signal That is, the reconstructed fluctuation segment data is obtained.

[0104] Step 5: Use RMSE and MPPE as evaluation indicators to evaluate the reconstruction accuracy. This method can achieve better compression reconstruction effect.

[0105] The reconstruction accuracy evaluation index formula of step 5 is:

[0106]

[0107]

[0108] Where T represents the time length corresponding to the data used; M i Indicates the size of the original data value at time i; M i ′ represents the size of the reconstructed data value at the corresponding time i; peak represents the daily peak data size.

[0109] The present invention is further described below by means of specific examples:

[0110] The experiment was conducted using REDD public data from American households, involving multiple types of electrical appliances such as ovens, refrigerators, dishwashers, lighting equipment, spin dryers, microwave ovens, electric heaters, etc. The data sampling frequency was 1Hz. This experiment selected the daily electricity consumption data of each household for data compression effect test and analysis. In terms of judging the data compression results, the reconstruction accuracy and compression rate were considered. On the one hand, the compression ratio CR was used to evaluate the amount of data reduction, and on the other hand, the reconstruction accuracy was measured by the two indicators of RMSE and MPPE. The compression method FLDC was used as a comparison method for the method proposed in this invention.

[0111] Table 1 Comparison of RMSE and MPPE of different methods

[0112]

[0113] As shown in Table 1, the three methods are compared in terms of reconstruction accuracy. RMSE and MPPE represent the error between the reconstructed data and the original data under different calculation methods. It can be seen that the method proposed in the present invention has a smaller reconstruction error and a higher reconstruction accuracy. Taking RMSE as an indicator, the reconstruction accuracy of the present invention can reach 99.7%. In the reconstruction process, the FLDC method uses GVE to divide the ground state and the excitation state, which easily divides the low-amplitude fluctuation segment into the ground state and uses the same value for reconstruction. The method used in the present invention can perform reasonable data compression on data in different states, reducing the occurrence of such problems. The average compression ratio of the method proposed in this article is 28.3, which is better than the average compression ratio of 9.89 of the FLDC method. Therefore, while retaining key information as much as possible, this method improves the degree of compression, reduces communication bandwidth, and alleviates communication pressure, achieving good compression effects.

[0114] It should be emphasized that the embodiments of the present invention are illustrative rather than restrictive. Therefore, the present invention includes but is not limited to the embodiments described in the specific implementation modes. Any other implementation modes derived by those skilled in the art based on the technical solutions of the present invention also fall within the scope of protection of the present invention.

Claims

1. A method for compressing data in a power system load fluctuation segment based on compressed sensing, characterized in that: The following steps are involved: Step 1: Based on the available load power consumption data, event monitoring is performed through edge detection algorithm to divide the event segment into the event segment and the non-event segment; Step 2, extract the non-event segment after the division in step 1, and further divide it, use the fluctuation detection algorithm to further detect the fluctuation segment data, and then divide the non-event segment into a fluctuation segment and a stable segment; Step 3: compress the fluctuation segment data extracted in step 2 by using a data compression and reconstruction method based on compressed sensing; Step 4: for the compressed fluctuation segment data obtained in step 3, the original data of the fluctuation segment data is reconstructed by using the optimized SAMP method; Step 5: Use RMSE and MPPE as evaluation indicators to evaluate the reconstruction accuracy.

2. The method for compressing data of load fluctuation segments of a power system based on compressed sensing according to claim 1 is characterized in that: The specific method of step 2 is: The voltage effective value detection method is used to extract the power system fluctuation segment data, and the remaining part of the non-event segment is the stable segment. The effective value of the voltage signal in the sliding window is calculated and compared with the preset threshold to detect the part corresponding to the fluctuation segment and extract the fluctuation segment: Determine the time length of the sliding window. The reference value is 0.5s-4s. The window length can be adjusted according to the specific data characteristics. For each sliding window, calculate the effective voltage value of the voltage signal within the window: Where x is the voltage value of the kth sampling point in the window; N is the number of sampling points in the window. The threshold is set based on statistical characteristics or experience, and the threshold is set to the voltage effective value plus the standard deviation: V=μ+ασ Among them, μ is the mean value, σ is the standard deviation, and α is usually 1 or 2, which can be adjusted according to actual needs; For each sliding window, it is judged whether its effective value exceeds the threshold. If the effective values ​​of multiple consecutive windows exceed the threshold, they are merged into a fluctuation segment, and the corresponding start time and end time are recorded. The fluctuation segment is extracted, and the remaining part is the stable segment, thereby realizing the division of non-event segments into fluctuation segments and stable segment data.

3. The method for compressing data of load fluctuation segment of power system based on compressed sensing according to claim 1, characterized in that: In the step 3, in terms of sparse basis optimization, a redundant dictionary MOD method is used to optimize the sparse basis, and a Gaussian matrix is ​​used as a measurement matrix; The specific steps include: (1) Initialization: setting the initial dictionary Ψ0 = Ψ, extracting characteristic signals from the power operation equipment, performing vector normalization, and generating the initial dictionary; (2) Input the training set and the number of dictionary atoms into the system. The training set is the original signal collected from the power system. The number of dictionary atoms should be greater than the dimension of the original signal itself so that there is sufficient expression ability to perform diversified representation of the power signal. (3) Perform learning iterations, and iterate the information input into the system under the following constraints: (4) After iteration, At this point, learning is stopped, and the obtained dictionary and the corresponding sparse coefficient matrix are output to obtain a compressed representation of the fluctuation segment data after compression processing.

4. The method for compressing data of load fluctuation segment of power system based on compressed sensing according to claim 1, characterized in that: The specific steps of step 4 include: a) Input: The following parameters are used: number of iterations t = 1; residual r0 = y, which is the low-dimensional representation of the compressed power load data; matching matrix A = ΦΨ (A∈R M×N ); step sequence s; variable initialization i=1; index set Initial step length L = γ t ; Adjustment factor γ = linspace(F,E,D), Where F = arctan(s) × M / 4π; E = s; D = M / 4; b) Discrimination: residual calculation u t = {u t |u t =| <r t-1 ,a t >|,1≤j≤N}, take out the column number set S k ={j|max(u j ,L)}, find the column number with the largest correlation with the residual; c) Atom candidate set update: add the column number set selected in the current iteration to the index set of the previous round to generate a new atom candidate set: t =Λ t-1 ∪S k , A t =a j ,j∈C k ; Update the estimated value of the signal sparse representation coefficient: d) Update the support set: Let A tk Use the corresponding A t The K columns in are represented by Λ tk Representation; residual update: e) Update the number of iterations and determine whether to terminate. If ||r t ||2→0, stop iteration and go to step h); otherwise, execute the next step; f) If || r t ||2<||r t-1 ||2, and L<N, then update the step size, L=L+γ t , γ=linspace(F,E,D)t=t+1, return to step b); g) If || r t ||2>||r t-1 ||2, and L<N, then update the step size, t=t+1, return to step b); otherwise, go to step h); h) Estimation Set Λ t Put non-zero items in Store the iteration value in and reconstruct the signal That is, the reconstructed fluctuation segment data is obtained.

5. The method for compressing data of load fluctuation segment of power system based on compressed sensing according to claim 1, characterized in that: The reconstruction accuracy evaluation index formula of step 5 is: Where T represents the time length corresponding to the data used; M i Indicates the size of the original data value at time i; M i ′ represents the size of the reconstructed data value at the corresponding time i; peak represents the daily peak data size.

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