A load scene generation method in an electric power supply guarantee background
By combining triple constraint screening and four-time period classification with the SA-WCGAN algorithm, a high-coverage and high-precision power supply load scenario was generated, which solved the problems of inaccurate generation and low efficiency in traditional methods, and supported the safe and stable operation and real-time control of the power grid.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA AGRI UNIV
- Filing Date
- 2026-02-10
- Publication Date
- 2026-06-12
AI Technical Summary
Traditional load scenario generation methods cannot accurately capture the diverse uncertainties and characteristics of loads under the background of power supply security, which makes it difficult to ensure the safe and stable operation and real-time control of the power grid. Existing methods rely on multiple sample data and are computationally complex, resulting in insufficient accuracy and efficiency in generating scenarios.
By employing triple supply guarantee constraint screening, four-period peak classification, and an improved SA-WCGAN algorithm, load data that meets the three constraints is screened out through preprocessing of historical load, new energy, and traditional unit data. The SA-WCGAN algorithm is then used to generate load scenarios with high coverage and high accuracy.
It achieves efficient generation of load scenarios that meet the power supply needs, solving the problems of inaccurate screening, missing classification, and low generation efficiency in traditional methods. The output scenarios can directly support power supply decision-making.
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Figure CN122196772A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system operation and control, and in particular to a method for generating load scenarios under the background of power supply security. Background Technology
[0002] Load scenario generation is fundamental to power system operation and dispatch. By generating load scenarios, load change characteristics can be better extracted, and the suitability of current grid generation plans and grid operation can be examined based on these characteristics, thus helping power companies optimize generation plans and grid operation. With the increasing installed capacity of new energy sources, electricity demand assessment has shifted from load evaluation to the assessment of the demand base for the source-load balance. The characteristics of the demand base for the source-load balance have entered the scope of power system operation and dispatch. By generating load scenarios with high coverage, distinct characteristics, significant impact, and compliance with the physical constraints of the power system, the dispatch center can comprehensively consider the electricity demand gap, source-load ramp-up capacity, and safety margin capacity at the day-ahead / intra-day stage, further optimizing unit control and generation schemes to maintain the balance and stability of electricity demand in the power system. Considering the electricity market, highly reliable, highly comprehensive, and highly accurate scenarios are one of the foundations of comprehensive electricity price adjustment schemes and electricity market regulation. The generation of load scenarios under the background of power supply security needs to comprehensively consider the characteristics of load fluctuation, peak value, and correlation with new energy sources under the power supply security scenario. The load scenario under this scenario can provide early warning information for subsequent power supply security. As a load characteristic scenario, it can be compared with the load information collected in real time over 15 minutes to become an early warning signal for power supply security. In general, load scenarios are not only the basic information for the safe operation of the system, but also a key technology for power supply security in the context of energy transition.
[0003] Currently, with increasing electricity demand and a further rise in the proportion of distributed energy connected to the grid, the difficulty of ensuring power supply is escalating. The load curve at 15-minute resolution exhibits a three-dimensional salient feature of "prominent peaks - large peak-valley differences - high ups and downs." Traditional methods of dividing load scenarios based on seasons can no longer capture the increasingly significant multivariate uncertainties of the load, posing a great challenge to the safe and stable operation of the power grid and its real-time control. In order to more accurately characterize the load uncertainty and multivariate features under the background of power supply, many methods have been provided at home and abroad, including fitting methods, Monte Carlo sampling, and Latin hypercube sampling. Among them, with the evolution of intelligent algorithms, machine learning has gradually become dominant in scene generation methods. Deep learning algorithms can solve the problems of small scene generation scale, slow generation speed, and insufficient generation coverage of traditional methods. By introducing intelligent algorithms, load scene generation is increasingly developing towards high coverage, large scale, and high feature satisfaction.
[0004] Currently, there are few methods for generating load scenarios under the background of power supply guarantee, both domestically and internationally. Existing technologies include methods that analyze and describe load data in supply guarantee scenarios based on several feature dimensions such as seasonality and the presence of large-scale events. However, these methods are highly dependent on multi-sample data, computationally complex, and do not sufficiently and accurately extract load features under the supply guarantee scenario. Summary of the Invention
[0005] To address the shortcomings of existing technical solutions, this invention provides a method for generating load scenarios under the background of power supply security, comprising the following steps: A. Data Filtering Layer: Preprocessing is performed on existing 15-minute resolution historical load time series data, renewable energy output data, and traditional unit output data to supplement missing parts of the three sets of data, resulting in historical load time series data that are consistent across the same time scale for the same region. L(t) Time series of new energy power output P renew (t) and traditional unit output time series P_R(t) ( t =1,2,3,...T, where T is the number of time points); based on the load characteristics under the power supply guarantee scenario, and considering the load ramping capability. LR With the generator set's climbing ability RR Comparison of fluctuations and instability, and the demand sequence based on the source-load balance after subtracting renewable energy output from the load. P net ( t ) and peak output of traditional units P conv , peak The comparison considers three scenarios: peak load exceeding limits, spatial negative correlation between load and renewable energy output, and mutual exclusion of renewable energy sources. Using the load characteristics under these three scenarios as constraints, the preprocessed load time series is analyzed. L(t) After filtering, daily load data that meets the three constraints is obtained. L sel ( t ); B. Feature Segmentation Layer: Establish a feature segmentation system, and classify the load data selected from the upper layer according to the differences in the dominant form of peak load under the supply guarantee scenario. L sel ( t The data was divided into four categories: morning peak-dominated, midday peak-dominated, evening peak-dominated, and combined peak-dominated. These four categories describe the differences in the timing of the supply guarantee scenario during the supply guarantee period. The four types of load data are denoted as follows: L sel ( t ) Ⅰ ,L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ ; C. Scene Generation Layer: Four types of payload data obtained from the feature segmentation layer L sel ( t ) Ⅰ , L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ Each is compared with random noise N~λ(0,1) (dimension is...) k , k =100-500), feature constraints C =( R constraint , P constraint , ρ constraint Mapped to the same space, the data serves as input to the SA-WCGAN algorithm model. This model expands the sample support set using random noise as a perturbation variable and employs feature constraints as condition vectors of the same dimension as the random noise to constrain the scene generation boundary, forcing the generator to sample within the feasible region. Through continuous iteration between the generator and discriminator, four sets of load scenarios satisfying the feature constraints are generated, representing load scenarios under the supply guarantee context. L (s) gen ( t ) Ⅰ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t ) Ⅱ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t )Ⅲ ( s= 1,2,... S, S (number of scenes generated) and L (s) gen ( t ) Ⅳ ( s= 1,2,... S, S (The number of scenes generated).
[0006] Furthermore, in step A, based on the historical load time series and the output time series of new energy units in the same region and at the same time scale, the demand time series of the source-load balance base is calculated, satisfying the following formula: ; in: For the source-load balance base demand sequence, For load time series, This refers to the new energy output sequence that has no outliers within the same region as the load sequence at the same time.
[0007] Further, in step A, based on the obtained source-load balance base demand sequence and the traditional generator output sequence, the ramp-up capabilities of the two are calculated and compared. The comparison results are used as the constraint basis for the fluctuation instability characteristics. The ramp-up capability calculation satisfies the following formula: ; ; in: For a moment t The source load balance base demand value, For a moment t The output value of traditional generator sets, This represents the base demand value for source-load balance at the previous moment. This represents the output value of the traditional generator set at the previous moment. The time resolution of the data is set to 15 minutes. and for t The load at any given time and the respective ramp-up capabilities of traditional generator units; Based on the demand of the source-load balance base and the ramping capability of traditional generator sets, the following criteria are used to determine whether load fluctuations exceed the unit's regulation capability: ;
[0008] in: k 1 is the climbing capacity safety factor, which is adjusted according to the set safety margin and is set to 1.1-1.5. When the judgment condition is met, the load fluctuation is considered unstable. Furthermore, in step A, multiple peak points are selected based on the traditional unit time series, and historical output peaks are filtered out. P conv , peak Based on historical peak output, the load time series is analyzed to identify load data that exceeds the peak limit. The criteria for this identification are as follows: ;
[0009] in: k 2. The safety factor, which takes into account the safety margin, is set to 0.7-0.9. When the judgment condition is met, the load peak is considered to be out of limit.
[0010] Furthermore, in step A, the determination of the mutual exclusion characteristics of new energy sources is achieved by constructing a similarity-exclusion matrix between the load and the new energy source sequence, as shown in equation (6): ; The off-diagonal elements of the similarity-repulsion matrix represent the correlation coefficients between the load sequence and the renewable energy sequence. When the correlation coefficient is a negative number close to -1, a strong negative correlation is considered to exist between the load and renewable energy output, indicating mutual repulsion between the two sources. The correlation coefficient calculation follows the Pearson correlation coefficient r formula: ; in, μ_L It is a load sequence L The mean, μ_renew It is a new energy power output sequence P renew The mean, Σ This indicates all time points t From 1 to T Sum.
[0011] Furthermore, in step B, the load peaks are further classified according to the time periods in which they occur, using the following classification formula: ;
[0012] in: This is a load peak classification determination value. When its value is 1, it means that the load peak is of the morning peak type; when its value is 2, it means that the load peak is of the afternoon peak type; when its value is 3, it means that the load peak is of the evening peak type; and when its value is 4, it means that the load peak is of the combined type. This is the upper limit for the start of the morning peak, with a value of 6:00. The lower limit for the end of the morning peak is set at 9:45. This is the upper limit for the midday peak start time, set at 9:45. The lower limit for the end of the midday peak is set at 13:45. The upper limit for the start of the evening rush hour is set at 17:00. The lower limit for the end of the evening peak is set at 20:45. The classification of load peaks can enhance the peak characteristics of load data in different time periods in subsequent models. The filtered daily load data is used as a classification sample. The proportion of time periods in the daily load data where supply guarantee scenarios occur is calculated. If the proportion exceeds 40% in the corresponding time period of the classification, the load data is considered to conform to the peak-dominated type of that time period. Based on this judgment system, the load data is divided into... L sel ( t ) Ⅰ , L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ Four categories; Further, in step B, the four types of load data after classification are normalized based on the MaxAbs normalization formula, mapping the data to the interval [-1, 1], which serves as the input to the feature extraction layer and satisfies the following formula: ;
[0013] in: L_norm ( t () represents the normalized sequence of load data. L_ max _ab s is the absolute value of the maximum value in the load sequence, i.e., | L_ max _abs |=max(| L 1|,| L 2|,...,| L n |); Furthermore, in step C, the iteration termination condition of the improved SA-WCGAN algorithm is: the discriminator loss function value ≤ 0.1 and the generator loss function value ≤ 0.2, or the number of iterations reaches 5000-10000.
[0014] Furthermore, the number of generated load scenarios S is 100-1000 sets, and each set of scenarios contains 96 time points.
[0015] Compared with the prior art, the advantages of this invention are: This invention proposes for the first time a closed-loop architecture of "triple supply guarantee constraint screening - four-period peak classification - efficient generation by SA-WCGAN algorithm": the screening stage focuses on the core risks of fluctuation instability, peak exceeding the limit, and mutual exclusion of new energy sources; the classification stage adapts to the scheduling needs of different time periods; and the generation stage achieves large-scale, high-fidelity, and fast scenario output through intelligent algorithms. This solves the pain points of traditional methods such as inaccurate screening, missing classification, and low generation efficiency. The output scenarios can directly support power supply guarantee decisions. Attached Figure Description
[0016] Figure 1 This is a flowchart illustrating the load scenario generation method based on the improved SA-WCGAN algorithm under the background of power supply security of the present invention. Detailed Implementation
[0017] To make the objectives, advantages, and features of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be emphasized that the above drawings and the following description are merely exemplary and not intended to limit the scope of the present invention or its application.
[0018] The present invention will be further described in detail below with reference to the accompanying drawings.
[0019] I. Basic Parameter Settings 1. Data Specifications: Historical load time series data, renewable energy output data and traditional unit output data are all 15-minute resolution, containing 96 time points per day (24h × 4 15-minute time periods). All three types of data correspond to the same provincial power grid area, with precise time alignment and no cross-regional or cross-time period data mixing.
[0020] 2. Core parameters: Climbing ability and safety factor k 1 =1.2, peak value over-limit safety factor k 2 =0.9; random noise N follows a λ(0,1) normal distribution with dimension k=250 (range 100-500); the SA-WCGAN algorithm terminates when the discriminator loss function value ≤0.1 and the generator loss function value ≤0.2, or when the number of iterations reaches 5000-10000; the number of generated scenes S=500 sets (range 100-1000 sets), and each set of scenes contains 96 load data points with a resolution of 15min.
[0021] 3. Data preprocessing method: Missing values are filled using linear interpolation and outliers are removed to ensure that the preprocessed data meets the accuracy requirements of subsequent calculations.
[0022] II. Data Filtering 1. Data preprocessing: Missing values were imputed and outliers were removed from the three types of raw data to obtain historical load time series with consistent time scales for the same region. L(t) Time series of new energy power output P_ renew (t) and traditional unit output time series P_R(t) (t=1,2,...,T, where T is the total number of time points).
[0023] 2. Calculation of the demand for the load balance base: Calculated according to formula (1), ;
[0024] in: For the source-load balance base demand sequence, For load time series, This refers to the new energy output sequence that has no outliers within the same region as the load sequence at the same time.
[0025] 3. Triple constraint judgment: ① Fluctuation instability judgment: Based on the obtained source-load balance base demand sequence and the traditional generator output sequence, the ramp-up capacity of the two is calculated and compared. The comparison result is used as the constraint basis for fluctuation instability characteristics. The ramp-up capacity calculation satisfies the following formula: ; ;
[0026] in: For a moment t The source load balance base demand value, For a moment t The output value of traditional generator sets, This represents the base demand value for source-load balance at the previous moment. This represents the output value of the traditional generator set at the previous moment. The time resolution of the data is set to 15 minutes. and for t The load at any given time and the respective ramp-up capabilities of traditional generator units; Based on the demand of the source-load balance base and the ramping capability of traditional generator sets, the following criteria are used to determine whether load fluctuations exceed the unit's regulation capability: ; in: k 1 is the safety factor for ramping capability, which is adjusted according to the set safety margin. It is set to 1.2. When the judgment condition is met, the load fluctuation is considered unstable. ② Peak value exceedance judgment: Select multiple peak points based on traditional unit time series data, and filter out historical output peak values. P conv , peak Based on historical peak output, the load time series is analyzed to identify load data that exceeds the peak limit. The criteria for this identification are as follows: ;
[0027] in: k 2 is a safety factor that takes into account the safety margin, set to 0.9. When the judgment condition is met, the load peak is considered to be out of limit.
[0028] ③ New energy mutual exclusion judgment: The judgment of the mutual exclusion characteristics of new energy is achieved by constructing a similarity and mutual exclusion matrix between the load and the new energy sequence, as shown in equation (6): ; The off-diagonal elements of the similarity-repulsion matrix represent the correlation coefficients between the load sequence and the renewable energy sequence. When the correlation coefficient is a negative number close to -1, a strong negative correlation is considered to exist between the load and renewable energy output, indicating mutual repulsion between the two sources. The correlation coefficient calculation follows the Pearson correlation coefficient r formula: ; in, μ_L It is a load sequence L The mean, μ_renew It is a new energy power output sequence P renew The mean, Σ This indicates all time points t From 1 to T Sum.
[0029] 4. Filtering Results: Daily load data that simultaneously meet the above three constraints are retained and denoted as... L sel (t) .
[0030] III. Scene Generation 1. Input Mapping: Normalizing the four types of load data L_ norm (t) Random noise and feature constraints are mapped to the same space.
[0031] 2. SA-WCGAN Algorithm Training: The mapped input data is fed into the SA-WCGAN algorithm model. The model expands the sample support set by using random noise as a perturbation variable, and uses feature constraints as condition vectors of the same dimension as the random noise to constrain the scene generation boundary. The iteration termination condition of the SA-WCGAN algorithm is: the discriminator loss function value ≤ 0.1 and the generator loss function value ≤ 0.2, or the number of iterations reaches 5000-10000.
[0032] 3. Scenario Output: Generate a set of four types of load scenarios that satisfy the triple constraints, i.e., load scenarios under the background of ensuring supply. L (s) gen ( t ) Ⅰ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t ) Ⅱ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t ) Ⅲ ( s= 1,2,... S, S (number of scenes generated) and L (s) gen ( t ) Ⅳ ( s= 1,2,... S, S (The number of scenes generated), each scene group contains 96 load data points at 15-minute resolution.
[0033] The contents not described in detail in this specification are existing technologies known to those skilled in the art.
Claims
1. A method for generating load scenarios under the background of power supply security, characterized in that, Includes the following steps: A. Data Filtering Layer: Preprocessing is performed on existing 15-minute resolution historical load time series data, renewable energy output data, and traditional unit output data to supplement missing parts of the three sets of data, resulting in historical load time series data that are consistent across the same time scale for the same region. L(t) Time series of new energy power output P renew (t) and traditional unit output time series P_R (t) ( t =1,2,3,...T, where T is the number of time points); based on the load characteristics under the power supply guarantee scenario, and considering the load ramping capability. LR With the generator set's climbing ability RR Comparison of fluctuations and instability, and the demand sequence based on the source-load balance after subtracting renewable energy output from the load. P net ( t ) and peak output of traditional units P conv , peak The comparison considers three scenarios: peak load exceeding limits, spatial negative correlation between load and renewable energy output, and mutual exclusion of renewable energy sources. Using the load characteristics under these three scenarios as constraints, the preprocessed load time series is analyzed. L(t) After filtering, daily load data that meets the three constraints is obtained. L sel ( t ); B. Feature Segmentation Layer: Establish a feature segmentation system, and classify the load data selected from the upper layer according to the differences in the dominant form of peak load under the supply guarantee scenario. L sel ( t The data was divided into four categories: morning peak-dominated, midday peak-dominated, evening peak-dominated, and combined peak-dominated. These four categories describe the differences in the timing of the supply guarantee scenario during the supply guarantee period. The four types of load data are denoted as follows: L sel ( t ) Ⅰ , L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ ; C. Scene Generation Layer: Four types of payload data obtained from the feature segmentation layer L sel ( t ) Ⅰ , L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ Each is compared with random noise N~λ(0,1) (dimension is...) k , k =100-500), feature constraints C =( R constraint , P constraint , ρ constraint Mapped to the same space, it serves as the input to the SA-WCGAN algorithm model. The SA-WCGAN algorithm model expands the sample support set by using random noise as a perturbation variable, and uses feature constraints as a condition vector with the same dimension as the random noise to constrain the scene generation boundary, forcing the generator to sample within the feasible domain. Through continuous iteration of the generator and discriminator, four sets of load scenarios that satisfy the feature constraints are generated, namely, load scenarios under the background of supply guarantee. L (s) gen ( t ) Ⅰ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t ) Ⅱ ( s= 1,2,... S, S (number of scenes generated) L (s) gen ( t ) Ⅲ ( s= 1,2,... S, S (number of scenes generated) and L (s) gen ( t ) Ⅳ ( s= 1,2,... S, S (The number of scenes generated).
2. The method for generating load scenarios under the background of power supply guarantee as described in claim 1, characterized in that, In step A, based on the historical load time series and the output time series of new energy units in the same region and at the same time scale, the base demand time series for source-load balance is calculated, satisfying the following formula: ; in: For the source-load balance base demand sequence, For load time series, This refers to the new energy output sequence that has no outliers within the same region as the load sequence at the same time.
3. The method for generating load scenarios under the background of power supply guarantee as described in claim 1, characterized in that, In step A, based on the obtained source-load balance base demand sequence and the traditional generator output sequence, the ramp-up capabilities of the two are calculated and compared. The comparison results are used as the constraint basis for the wave instability characteristics. The ramp-up capability calculation satisfies the following formula: ; ; in: For a moment t The source load balance base demand value, For a moment t The output value of traditional generator sets, This represents the base demand value for source-load balance at the previous moment. This represents the output value of the traditional generator set at the previous moment. The time resolution of the data is set to 15 minutes. and for t The load at any given time and the respective ramp-up capabilities of traditional generator units; Based on the demand of the source-load balance base and the ramping capability of traditional generator sets, the following criteria are used to determine whether load fluctuations exceed the unit's regulation capability: ; in: k 1 represents the climbing capacity safety factor, which is adjusted according to the set safety margin and is set to 1.1-1.
5. When the judgment condition is met, the load fluctuation is considered unstable.
4. The method for generating load scenarios under the background of power supply guarantee as described in claim 1, characterized in that, In step A, multiple peak points are selected based on the traditional unit time series, and historical output peaks are filtered out. P conv , peak Based on historical peak output, the load time series is analyzed to identify load data that exceeds the peak limit. The criteria for this identification are as follows: ; in: k 2. The safety factor, which takes into account the safety margin, is set to 0.7-0.
9. When the judgment condition is met, the load peak is considered to be out of limit.
5. The method for generating load scenarios under the background of power supply guarantee as described in claim 1, characterized in that, In step A, the determination of the mutual exclusion characteristics of new energy sources is achieved by constructing a similarity-exclusion matrix between the load and the new energy source sequence, as shown in equation (6): ; The off-diagonal elements of the similarity-repulsion matrix represent the correlation coefficients between the load sequence and the renewable energy sequence. When the correlation coefficient is a negative number close to -1, a strong negative correlation is considered to exist between the load and renewable energy output, indicating mutual repulsion between the two sources. The correlation coefficient calculation follows the Pearson correlation coefficient r formula: ; in, μ_L It is a load sequence L The mean, μ_renew It is a new energy power output sequence P renew The mean, This indicates all time points. t From 1 to T Sum.
6. The method for generating load scenarios under the background of power supply guarantee as described in claim 1, characterized in that, In step B, the load peaks are further classified according to the time periods in which they occur. The classification formula is as follows: ; in: This is a load peak classification determination value. When its value is 1, it means that the load peak is of the morning peak type; when its value is 2, it means that the load peak is of the afternoon peak type; when its value is 3, it means that the load peak is of the evening peak type; and when its value is 4, it means that the load peak is of the combined type. This is the upper limit for the start of the morning peak, with a value of 6:
00. The lower limit for the end of the morning peak is set at 9:
45. This is the upper limit for the midday peak start time, set at 9:
45. The lower limit for the end of the midday peak is set at 13:
45. The upper limit for the start of the evening rush hour is set at 17:
00. The lower limit for the end of the evening peak is set at 20:
45. The classification of load peaks can enhance the peak characteristics of load data in different time periods in subsequent models. The filtered daily load data is used as a classification sample. The proportion of time periods in the daily load data where supply guarantee scenarios occur is calculated. If the proportion exceeds 40% in the corresponding time period of the classification, the load data is considered to conform to the peak-dominated type of that time period. Based on this judgment system, the load data is divided into... L sel ( t ) Ⅰ , L sel ( t ) Ⅱ , L sel ( t ) Ⅲ , L sel ( t ) Ⅳ Four categories.
7. The method for generating load scenarios under the background of power supply guarantee as described in claim 6, characterized in that, In step B, the four types of load data after classification are normalized based on the MaxAbs normalization formula, mapping the data to the interval [-1, 1], which serves as the input to the feature extraction layer and satisfies the following formula: ; in: L_norm ( t () represents the normalized sequence of load data. L_ max _ab s is the absolute value of the maximum value in the load sequence, i.e., | L_ max _abs |=max(| L 1|,| L 2|,...,| L n |).
8. The method as described in claim 1, characterized in that, In step C, the iteration termination condition of the improved SA-WCGAN algorithm is: the discriminator loss function value ≤ 0.1 and the generator loss function value ≤ 0.2, or the number of iterations reaches 5000-10000.
9. The method as described in claim 1, characterized in that, The number of generated load scenarios S is 100-1000, and each scenario contains 96 time points.