CN110533304B

CN110533304B - Power system load uncertainty analysis method

Info

Publication number: CN110533304B
Application number: CN201910738526.2A
Authority: CN
Inventors: 刘绚; 朱鑫; 车亮; 范维
Original assignee: Hunan University; Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
Current assignee: Hunan University; Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
Priority date: 2019-08-12
Filing date: 2019-08-12
Publication date: 2022-12-09
Anticipated expiration: 2039-08-12
Also published as: CN110533304A

Abstract

The invention discloses a method for analyzing load uncertainty of a power system, which decomposes a load sample into a typical scene (a central sample), an extreme scene (an extreme sample) and a common scene (a common sample). To ensure robustness, the extreme scenario (extreme sample) is used to determine the crew composition scheme; the corresponding scheduling problem is computed using the typical scenario (center sample) with higher probability of occurrence. In view of the characteristic that each load sample is high-dimensional data, the PCA technology is adopted to reduce the original load sample to a low-dimensional space so as to better reveal the relationship between the data. Therefore, a scheduling scheme with high robustness and economy can be obtained.

Description

Power system load uncertainty analysis method

Technical Field

The invention relates to the field of machine learning, in particular to a method for analyzing load uncertainty of a power system.

Background

Nowadays, with the development of economic society, the demand for electric power is sharply increasing. The advent of new load sources, such as high speed railways and electric cars, has created significant difficulties in load prediction. These difficulties are mainly due to the very variable nature of these loads. However, the conventional unit combination determines the on/off state of the generator through a determined load prediction value. Uncertainty due to load prediction error is not considered. However, load uncertainty presents significant challenges to the economics and reliability of the power grid, such as frequency droop, transmission line overload, cascading failures even when the system is in a heavy load condition, and the like. To effectively solve this problem, researchers have proposed a number of solutions, of which random optimization [1] - [11] and robust optimization [12] - [17] are commonly used to deal with this type of problem.

Stochastic optimization is a stochastic scenario-based optimization method that generates a large number of scenarios to model the uncertainty of the load. Monte Carlo (MC) is a typical emulation method. In document [7], wu et al propose a scenario-based model for calculating long-term safety-constrained crew combinations. Where MC is used to generate a large number of scenes, simulating uncertainty changes in load. In document [8], wang et al propose a scene-based safety constraint unit combination model to deal with the intermittency and volatility problems of wind power. Wherein, the output of the wind power is simulated by utilizing the MC. In document [9], wu et al propose a scene simulation method under a multi-time scale condition. And the scheduling plan is calculated by using the method to solve the problem of load prediction uncertainty. Another stochastic optimization method is opportunistic constraint optimization, which deals with load uncertainty by placing probabilistic constraints on possible load scenarios. Wu et al, in [10], propose a unit combination model of opportunity constraints to solve the influence of load prediction uncertainty on transmission line overload and power imbalance. In document [11], wang et al propose a new model for optimizing the Unit Combination (UC) solution by adjusting the system risk threshold, in combination with opportunity constraints and objective planning. The random optimization has a fatal disadvantage that some possible load scenarios are not considered, especially some extreme load scenarios, so that the robustness of the unit combination scheme is poor. In addition, in order to ensure the accuracy of the unit combination scheme, a large number of scenes need to be generated, which brings huge burden to the calculation.

Robust optimization is another way to handle load randomness. The purpose of the robust optimization is to calculate the unit combination scheme under the worst scenario. This scheme can cope with any scenario if the dispatch plan can be satisfied in the worst case. This type of problem can be expressed as a min-max-min linear optimization problem, where the worst case is determined in the middle layer. The entire optimization problem can be solved by a decomposition algorithm. But the solution complexity is high. In document [14], hu et al propose a multi-band robust optimization unit combination model to solve the problem of time correlation of load uncertainty. In document [15], hu et al propose a robust optimization model to minimize the scheduling cost to ensure that the scheduling plan can be safely adjusted in real time as the load fluctuates within the predicted interval. In [16], bertsimas et al propose a phase-adaptive robust optimization model that considers load uncertainty issues in both power and demand after uncertainty subsets are determined. Due to the worst case considerations, the corresponding unit combination scenario will be very conservative, i.e. the operating costs are too high. In order to reduce costs. Blanco et al propose a method for partitioning the worst scenario in [17] for solving a scenario-based two-phase safety constraint unit combination model. This approach only considers the worst scenario partitioning for reducing the conservatism of the scheduling scheme. The conservatism of the scheduling scheme calculated by the method depends on the number of scene partitions, but the number of the scene partitions is set manually. This results in the method being less scientifically rigorous for dividing the scene. And only the worst case is considered, and other scene information is not fully utilized.

In addition, some other optimization methods have been proposed in recent years. Wherein interval optimization [18] - [20] simply considers the uncertainty of these variables within the prediction interval, ignoring the probability distribution of these variables. In document [21], zhao et al propose weight components based on robust optimization and stochastic optimization to reduce conservatism. The method only simply combines the objective functions of robust optimization and random optimization through weight components, and does not deeply research the internal relation between the two methods. Xiong et al propose a distributed robust two-stage crew portfolio model in [23] that deals with load uncertainty by defining fuzzy subsets. The aim of this method is to minimize the worst case expected total cost, much like the method in document [17 ]. These methods do not consider the relationship between scenes, and there is no explicit scene division method either. And the information of the scene is not sufficiently used. For example, robust optimization and some improved methods only consider the use of the worst scenario, ignoring the information of other scenarios. In addition, the scene division of all methods is performed on a high-dimensional space, and the characteristic that the relation between scenes is easily revealed in a low-dimensional space is ignored.

Disclosure of Invention

The invention aims to provide a method for analyzing the load uncertainty of a power system, and the robustness of a scheduling scheme is improved. In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method for analyzing uncertainty of load of a power system is characterized by comprising the following steps:

1) Removing redundant information in the historical load samples, and projecting the historical load samples with the redundant information removed into a low-dimensional space;

2) Dividing the historical load samples of each cluster in the low-dimensional space into extreme samples, common samples and central samples;

3) Returning all samples in the low-dimensional space divided in the step 2) to the original dimension, and reconstructing historical load sample data;

4) If the extreme samples in the historical load sample data obtained by reconstruction have a unit combination scheme, the unit combination scheme is reserved; otherwise, discarding the extreme sample;

5) Calculating whether each common sample and the center sample in the reconstructed historical load sample data have a corresponding economic dispatching scheme or not, and recording the score of each unit combination scheme reserved in the step 4); if the economic dispatching solution exists in the unit combination scheme under the common sample or the central sample, the fraction of the corresponding unit combination scheme is increased, the feasibility proportion of each unit combination scheme is calculated by using SI/NJ, the SI is the total fraction of each unit combination scheme, and the NJ is the total number of the common sample and the central sample;

6) Selecting the central sample with the maximum local density in each cluster to replace all sample information in the cluster; the probability of fluctuation of the load of the power system is shown through the occurrence probability of the center sample of each cluster and the corresponding cluster; selecting a unit combination scheme with the maximum SI score, and calculating an economic dispatching result of each central sample according to the unit combination scheme; and finally, combining the calculation results of all the central samples through the occurrence probability of the corresponding clusters to obtain a final scheduling plan.

In the step 1), redundant information in the historical load sample is removed by using a principal component analysis method.

In step 2), calculating the average density of the historical load samples in each cluster, if the local density of a certain historical load sample is greater than the average density, identifying the sample as a core sample, otherwise, identifying the sample as an edge sample, namely an extreme sample; the cluster center in the core sample is the center sample, and the others are the common samples.

In step 3), the historical load sample is reconstructed by using the following formula

Wherein,

S _s for the s-th load scenario, N is the number of load scenarios, Λ _m ＝[e ₁ ,e ₂ ,……,e _m ]， e ₁ ,e ₂ ,……e _τ Is a covariance matrix Δ S ^T The feature vector matrix of (a) is,

in the step 4), whether a unit combination scheme exists is judged through the following unit combination models:

wherein, F _i (p _its ) Shows the coal burning cost, SU, at the t-th moment of the ith unit in the scene s _its Representing the startup cost of the ith unit at the tth moment under the scene s, NG representing the number of coal-fired units, NT representing the planned time scale, and p _its Represents the output of the ith coal-fired unit at the t-th moment in the scene s, PD _ts Representing the load value, R, at time t under scene s _i Represents the upper limit of the slope climbing of the ith unit, p _min,i ,p _max,i Respectively representing the minimum and maximum output of the ith unit, I _its Represents the state of the unit i at the t-th moment in the scene s, X _on,i(t-1)s ,X _off,i(t-1)s Respectively represents the cumulative opening and closing time of the ith unit at the T-1 th moment in the scene s, T _on,i ,T _off,i Respectively representing the minimum startup and shutdown time required by the ith unit, wherein SF represents a system transfer factor matrix, K _p ,K _D Respectively representing unit and load node connection matrices, PL _max Representing the upper limit of the line power flow, wherein the matrixes are constant matrixes; p _ts ,PD _ts Respectively representing the output and the system load of the coal-fired unit at the time t of a scene s; the system transfer factor matrix SF is a constant matrix.

In step 6), the economic dispatch calculation is carried out by using the following formula:

where NS denotes the number of typical scenes, π _s Representing the probability of occurrence of the s-th typical scene.

Compared with the prior art, the invention has the beneficial effects that:

1) The invention provides a load uncertainty processing method based on machine learning, which has the advantage of generating a scheduling scheme with better economy while ensuring robustness. A large number of simulation experiments prove that the robustness of the unit combination scheme can be ensured by a small number of extreme scenes.

2) The load scenes are effectively divided into typical scenes, extreme scenes and common scenes, and the selected extreme scenes ensure the robustness of the unit combination scheme.

3) Projecting the load samples into a low-dimensional space using principal component analysis makes the load scenes easier to separate, as the result shows that some extreme load samples can be found quickly in some clustered samples and that the extreme load samples contain information of most common load scenes.

4) The calculated unit combination scheme has better robustness.

Drawings

Fig. 1 high-dimensional data (left) and low-dimensional data (right).

Fig. 2 decision diagram (left) and cluster diagram (right).

Fig. 3 scene separation and screening.

Figure 4 model solution flow diagram.

Fig. 5 compares the clustering results with PCA versus without PCA.

Fig. 6 PCA impacts dispatch plan robustness and economics.

FIG. 7 scores for the crew assembly scenario corresponding to each extreme sample.

FIG. 8 is a load curve for various methods.

Fig. 9 compares the robustness of the four methods.

Detailed Description

In order to overcome the defects of the random scene method, some extreme load scenes and typical scenes need to be considered, and the robustness of the scheduling scheme is improved under the condition of ensuring the economy. In this section, we adopt the method of CSFDP to separate the historical samples into edge samples, normal samples, and center samples. The edge samples represent extreme scenes of the load, the center samples represent typical scenes of the load, and the probability of occurrence is relatively high, while the normal samples represent normal scenes. Principal component analysis is introduced to project high-dimensional load samples into a low-dimensional space to better reveal the intrinsic connections between the samples.

The principal component analysis of the present invention is described below.

Typically, the data dimensions of the raw loads are high, especially in large power systems. Take IEEE 118 node system as an example. The system has 91 load nodes, so the data dimension of its 24-hour load scenario is 91 × 24=2184. High dimensional data not only computingThe volume is large and the internal connection between data is difficult to find. For example, the IEEE 188 node system has high-dimensional load sample data as shown in the left side of fig. 1. The data are completely overlapped, and the relationship between the data is difficult to reveal. In this regard, PCA [24]-[26]An efficient tool is provided for extracting key information by projecting raw data into a low-dimensional space. As shown in the right side of fig. 1, the relationship between the data is easily observed by reducing 118 the load sample of the system to two dimensions. As shown in the figure, the distance between the sample points reflects the similarity between two scenes, how many sample points in a certain area reflect the occurrence probability of the scene in the area, and many sample points have a high occurrence probability, and vice versa. When the PCA reduces the high-dimensional data to a low-dimensional space, most of the information of its original data will be preserved, as in the 118-node system, and 97% of the information of its original data is preserved in the low-dimensional space. The basic principle of PCA is described as follows: suppose there are n load nodes and t moments, so the S-th load scenario S _s Is n x t. Assuming there are N load scenes, then the average of the scenes is

Next, the difference between each load scene and the average value is calculated by formula (2).

On this basis, we can calculate the covariance matrix by (3).

And decomposing the covariance matrix to obtain the eigenvector matrix e = [ e ] ₁ ,e ₂ ,……e _τ ]And eigenvalue vector λ = [ λ ] corresponding to its eigenvector ₁ ,λ ₂ ,……λ _τ ]. Thus, the raw data is projected into a new space with dimensions of m (m ≦ n × t) by equation (4).

Wherein Λ _m From the slave _e M extracted feature vectors of Lambda _m ＝[e ₁ ,e ₂ ,……,e _m ]. Principal component analysis maps high-dimensional data into a low-dimensional space through the eigenvectors of the data itself, so their corresponding eigenvalues reveal how much of the original data information is kept in the new space. The feature vector of the largest eigenvalue contains the richest information in the original data, called Principal Component (PC). The percentage of information retained in the new space can be estimated by calculating the corresponding feature values.

Equation (5) calculates the situation where the information of the original data remains in the new coordinate system. Where m represents the dimension of the new coordinate and τ represents the dimension of the original coordinate. In order to solve the safety constraint unit combination model, the data must be calculated by (6) inverse transformation back to the original dimension.

This verifies that PCA not only reduces computational complexity, but also helps to reveal the intrinsic relationships between data. In actual calculations, at least 85% of the information needs to be retained to ensure the accuracy of the calculations. It should be noted that PCA can help reduce the dimensionality of the data, revealing the connections within the data, but cannot separate the load samples into certain categories. This is achieved by a fast search and find density peak clustering (the clustering by fast search and find of density peaks) algorithm.

The fast search and discovery density peak Clustering (CSFDP) algorithm of the present invention is as follows.

And mapping the original load data into a new low-dimensional coordinate system, and separating the low-dimensional samples. Fast search and find density peak clustering [27] can be used to separate scenes. Since the method has one important parameter, namely the local density. It represents how close the scene is to other surrounding scenes. This reflects the probability of occurrence of such a scene. The probability of occurrence for each scene can be calculated by this parameter. According to the difference of the local density (the size of the occurrence probability), the scenes can be divided into typical scenes, ordinary scenes and extreme scenes.

CSFDP is a method of clustering data with similar information by local density and distance. Local densities are calculated using gaussian kernels.

Wherein d is _c Denotes the truncation distance, d _jk Represents the distance between the jth data and the kth data, p _j Is the local density of the jth scene. To select the appropriate truncation distance, the distances between any two points are calculated and the calculated distances are arranged in ascending order, we have

Wherein θ ∈ [0.01 0.02 ]]，[Mθ]Indicating rounding off the value of M θ. The local density is an important parameter reflecting the occurrence probability of a scene. Another important parameter δ _j Denotes the minimum distance to the j point among all points whose local density is greater than j; if j is the maximum local density point, it represents the maximum distance to j among all the sample points. Will rho _j And delta _j Multiplying to obtain the formula (9)

γ _j ＝ρ _j ·δ _j j＝1,2,……,N (9)

Wherein gamma is _j Are important parameters for generating a decision graph for determining the cluster center. Arranging gamma in descending order _j The decision graph in the new coordinate system is shown in fig. 2.

It can be seen from the left diagram of fig. 2 that all the points arranged from right to left reflect the variation trend of the gamma value of the point. It can be seen that there is a clear jump in the gamma values for all points from below the dotted line to above the dotted line. It indicates that the points above the dotted line are all cluster centers, and the points below the dotted line are common points. These common points will be clustered by the cluster centers. The cluster centers are represented by solid dots in the right diagram of fig. 2, and the non-cluster centers are corresponding virtual center points.

The average density of these samples in each cluster is then calculated and taken as the lower threshold for the separation density of the load samples. In each cluster, a sample is identified as a core sample if its local density is greater than the average density, and as an edge sample otherwise. The cluster centers in the core samples are identified as center samples, and the others are normal samples. By this clustering algorithm, all load samples are divided into a plurality of clusters, and the samples are further divided into core samples and edge samples in each cluster. The core samples consist of the center samples, which occur with the highest probability in each cluster (the highest local density), and the normal samples, and thus they correspond to the typical scenario of the load. Also, normal samples with high density (high occurrence probability) represent normal scenes of the load; in contrast, edge samples represent extreme scenarios of loading due to their very low local density (lower probability of occurrence).

The sample isolation and screening process of the present invention is described below.

In a general scenario approach, a large number of scenarios will be used to calculate a group composition scheme to improve the reliability of the dispatch plan. Each scenario has its own characteristics that, if used indiscriminately, will affect the reliability of the scheduling scheme and increase the computational burden. In addition, some scenes have similar characteristics. If scenes with similar information are repeatedly computed in the computation of the scheduling scheme. They only increase the computational burden and do not contribute to the improvement of the dispatch plan.

However, these scenes can be divided according to the similar characteristics between them, and the typical features of each classification can be easily extracted. The safety constraint unit combination is calculated by using the typical characteristics of the scene, so that the reliability of the scheduling scheme is improved, and the calculation burden is reduced. Therefore, scene selection is necessary. At present, most methods only consider reducing scenes to reduce the calculation burden, do not consider the relationship among the scenes, and lack a clear method for distinguishing the scenes.

As shown in FIG. 3, in the present invention, we propose a method for explicit scene separation and screening. PCA is used to reveal the relationships between scenes, and CSFDP is used to separate scenes. The high dimensional original scene is projected into a two dimensional space while PCA preserves 97% of the information of the original data. The result after dimensionality reduction can be seen on the right side of fig. 1, where each point represents a scene. The distance between two points reflects the similarity between two scenes, and the number of points in a region reflects the probability of the region occurring. Thus, the relationship between the samples has been clearly revealed. These scenes are divided into several classes in a low-dimensional space by CSFDP, and the scenes of each cluster are further divided into typical scenes, general scenes, and extreme scenes according to local density (occurrence probability). And finally, returning the scenes to the original dimension through inverse PCA conversion for calculating a safety constraint unit combination model.

If the unit combination scheme can meet the extreme scenes, the unit combination scheme can also meet most normal scenes. To ensure the robustness of the dispatch plan, extreme scenarios must be selected for the calculations. While the typical scenario represents the maximum likelihood of a scenario occurring, it should be used to calculate an economic dispatch in order to improve the economic level. The two scenes are used together, so that the robustness and the economy of the dispatching plan can be well balanced.

The present invention relates to a safety restraint unit combination problem in the past.

After the load scenario is determined, the future safety constraint unit combination model can be described as the following formula:

subject to

wherein (10) represents an objective function, F _i (p _its ) Represents the cost of burning coal at the t-th moment of the ith unit in the scene s, SU _its Representing the boot cost of the ith unit at the tth moment under the scene s, NS representing the number of typical scenes, pi _s Representing the probability of occurrence of the s-th typical scenario, NG representing the number of coal fired units, NT representing the projected time scale, p _its Represents the output of the ith coal-fired unit at the t-th moment in the scene s, PD _ts Representing the load value, R, at time t under scene s _i Represents the climbing upper limit, p, of the ith unit _min,i ,p _max,i Respectively representing the minimum and maximum output of the ith unit, I _its Represents the state of the unit i at the t-th moment in the scene s, X _on,i(t-1)s ,X _off,i(t-1)s Respectively represent the ithThe time of the machine set on and off is accumulated at the T-1 th moment in the scene s, T _on,i ,T _off,i Respectively representing the minimum startup and shutdown time required by the ith unit, wherein SF represents a system transfer factor matrix, K _p ,K _D Respectively representing unit and load node connection matrices, PL _max Representing the upper limit of line flow, the above matrices are all constant matrices, P _ts ,PD _ts Respectively representing the output of the coal-fired unit and the system load at the time t of the scene s. (11) For power balance constraint, (12) for climbing constraint, (13) for generator output boundary constraint, (14) for minimum start-stop constraint, and (15) for line current constraint. As previously described, conventional crew assembly models do not account for load uncertainty. A good unit assembly solution should satisfy both economy and robustness. To ensure robustness, some extreme scenarios need to be considered, although their probability of occurrence is relatively low. Meanwhile, if an extreme case is included in the crew combination calculation, the operation cost should be controlled. The day-ahead safety constraint unit combination model is solved through a two-stage optimization problem. In a first phase, the on-off state of the generator is determined according to a selected extreme load scenario; in the second stage, an economic scheduling sub-problem of random security constraints is solved. The typical scenario is selected for calculating the sub-problem, thereby ensuring the economy of the scheduling scheme. The flow chart of this scheme is shown in figure 4.

The concrete solving steps are shown as the following chart:

the first step is as follows: redundant information in the historical data is removed by using principal component analysis. The raw data is projected into a two-dimensional space where at least 97% of the information is retained for use in subsequent safety-constrained fleet combination calculations.

The second step is that: the method of CSFDP is adopted to divide the historical load samples of each cluster into extreme samples, normal samples and central samples.

The third step: through (6) reconstructing load samples, returning the divided low-latitude scene data to the original dimensionality

The fourth step: each extreme sample is used to compute a group combining problem (16). If the extreme sample has a unit combination scheme, the unit combination scheme is reserved; otherwise, the sample will be discarded.

s.t constraints (11) - (15)

The optimization problem described above will be solved under each extreme scenario (extreme sample).

The fifth step: and 4, calculating whether each core sample (the general name of the central sample and the common sample) has a corresponding economic dispatching scheme, and recording the score of each unit combination scheme reserved in the step 4. If the crew composition solution has an economic Scheduling (SCED) solution in this core scenario, the score of the corresponding crew composition solution will increase (SI = SI + 1). And calculating the feasibility proportion of each unit combination scheme by using SI/NJ, wherein SI is the total score of each unit combination scheme, and NJ is the total core sample number.

And a sixth step: the crew composition scheme with the largest SI score is selected, by which the economic scheduling calculation is performed using the center sample of each cluster, which is modeled as (17).

s.t. constraints (11) - (13), (15)

Wherein pi _s Indicates the occurrence probability of the center sample, i.e., per cluster, and NS indicates the number of center samples, i.e., the number of all clusters. The on/off state of the unit is determined in the fourth step.

The dispatching plan calculated by the method has higher robustness and lower conservatism. The robustness of the scheme is enhanced by selecting extreme scenarios of the load, and only typical high probability load scenarios (central samples) are considered, ensuring the economy of the system. The effectiveness of the method will be verified in the case analysis of the next section.

We tested the proposed method using an IEEE 118 node system. Load data is from the 24 hour historical load of PJM 2017 to 2018 [28]. The simulation was performed on a personal computer with 8GB memory at 3.9GHz, and the model and algorithm were implemented in MATLAB.

As shown in the left panel of fig. 5, 241 sample scenes were involved in the experiment. The normal and extreme samples are represented by blue and green dots, respectively, and the red dot is the center sample (cluster center) of each cluster. In the upper left panel of fig. 5, the sample separation results produced by our method are shown. When the samples are separated using only CSFDPs, their clustering results are obtained in a high-dimensional space, but their classification results are projected into a two-dimensional space for easy direct observation, shown in the lower left diagram of fig. 5. Their respective 24 hour core and extreme samples are shown on the right of fig. 5. The green dotted line is extreme load sample data, and the cyan solid line is core load sample data. The extreme load sample (202) with the highest score using our method is represented by the solid black line in the upper right graph of fig. 5. In the lower right diagram of fig. 5, the solid black line represents the load sample data (190) that achieves the highest score using only CSFDP separation.

From the left half of fig. 5, we can see the distribution of the load samples in a two-dimensional coordinate system. Experimental results show that extreme samples (green dots) can be easily isolated using our method. In the upper left diagram of fig. 5, it is shown that the core sample is surrounded by the extreme sample, which is far from the area containing a large number of samples. In fact, the number of samples in a region reflects the occurrence probability of the samples in the region. In reality, the probability of occurrence of extreme samples is low. This means that extreme samples can be easily separated from the data using our method. In the lower left diagram of fig. 5, it can be seen that some extreme samples are separated in some regions with a large number of samples, and some extreme samples are not separated. As in the lower left diagram of fig. 5, which is the lower left region of the diagram, points that are significantly further away from the concentration region are not separated. This means that some extreme samples cannot be accurately separated using only CSFDP clustering. At the upper right of fig. 5, it can be seen that the 39 extreme samples selected by our method can cover the core sample, i.e. the cyan solid line area is covered by the green dashed line area and has a similar shape. This means that the extreme scenes contain information of normal scenes and typical scenes. Therefore, if the crew composition scheme can satisfy extreme scenarios, they are likely to also satisfy other common scenarios and typical scenarios. However, in the lower right diagram of fig. 5, we can see that the 51 extreme scenes using only CSFDP separation cannot be used to fully encompass those common scenes. This means that the extreme scenes using only CSFDP separation do not fully contain the information of the normal scenes. And we can see that the black solid lines chosen by the two methods are not at the highest position, but near the top, and the two solid black lines are not identical. This means that the two solid black lines contain the most abundant information of the common scene in the respective methods, but the amount of information contained in the two solid black lines is different, which affects the robustness of the unit combination scheme.

In the left diagram of fig. 6, it represents the proportion of the number of scenes that the unit combination scheme can be executed in the normal scene and the extreme scene. It can be seen from the figure that in the normal scene and the extreme scene, the scene proportion of the unit combination scheme calculated by the method can be executed is 1.00 and 0.94 respectively. This means that the crew composition scenario generated by our method can handle 100% of normal scenarios and 94% of extreme scenarios. However, the proportions in which the crew composition scheme calculated using only the CSFDP method can be performed are 1.00 and 0.84 in the normal scenario and the extreme scenario, respectively. This means that the robustness of the solution using only the CSFDP computer group combination is similar to that of our method computer group combination under common scenarios. But in extreme scenarios our method is more robust than the method using only CSFDP. In addition, the operating costs calculated for both methods are similar, and the operating cost of our method is 6649$/h (0.52% increase) higher than the cost of using only the CSFDP method. This means that our method can produce a more robust unit combination solution under similar economic conditions. The robustness of the calculated unit combination scheme can be influenced by the separation of the extreme scenes, and the accuracy of scene separation can be improved by the method.

The unit combination plan score for each extreme sample is shown in fig. 7. Where the size of a point is proportional to the value of the score and is distinguished by different colors. The largest black spot score is seen to be the highest, 202 points. The percentage of the number of scenes that the corresponding crew grouping scheme can be executed is 1.00. The samples out of the black dotted circle are samples for which the unit combination scheme cannot be calculated. An important observation can be found. The score in the figure increases gradually from left to right. This means that if we choose the sample on the right side of the graph, the calculated crew composition scheme can satisfy more load scenarios. This provides us with a fast method to identify load samples that can produce a highly robust crew composition scheme. That is, we only need to select the load sample on the right side of the figure.

To verify the effectiveness of this method, we compared it with the Monte Carlo (MC) method, the opportunistic constraint optimization method, and the worst scenario based robust optimization method. Using the exemplary scenario of fig. 5, the expected load of the opportunistic constraint is found by its probability weighted average. The line overload probability is set to 10% and the deviation to 4% of the expected value. The load curve is shown in the lower right-hand graph of fig. 8. The MC method will simulate to generate 3000 scenes, which are then reduced to 10 scenes in the bottom left of fig. 8 by a scene reduction technique. And the upper right graph of figure 8 shows the load curve obtained using our method.

As can be seen in FIG. 8, the load curves obtained for PCA and CSFDP are smooth and their shapes closely approximate the shape of the historical load. But the MC method generates an irregularly shaped load curve. In addition, the Monte Carlo (MC) simulated scenes are mainly concentrated in regions with high probability. Extreme scenarios are difficult to simulate, and the opportunity constraint optimization method mainly considers expected values of loads and does not consider some necessary extreme scenarios. In contrast, our approach fully considers some extreme scenarios to ensure the robustness of the bank combining scheme.

TABLE I running costs of the four methods

We will compare the economics and robustness of the four method crew combination scheme. The operating costs of the four processes are given in table i. Where the third and fourth columns are the running cost offset and the corresponding percentage increase/decrease, respectively. Compared with our method, the opportunistic constraint method has the lowest cost, and the worst scenario method has the highest cost. The cost of our approach has approached the cost of MC simulation and opportunity constrained approaches. The cost of our method is 7113$/h (0.56%) higher than that of the Monte Carlo simulation method, and is 55996$/h (4.55%) higher than the operation cost of the opportunity constraint method. The cost of the method is lower than that of a worst scenario-based method by 638451$/h, and the operation cost is reduced by 33.18%.

Our approach has advantages over other approaches in terms of the robustness of the fleet combination solution. It can be seen from fig. 9 that the number of feasible scenarios of our method is much larger than the monte carlo and chance constraint methods in normal scenarios and extreme scenarios. In particular, our method can achieve a unit combination solution with the same robustness as the worst scenario based method. For example, the number of feasible scenarios of our method and the worst scenario based method is 202 in the normal scenario and 37 in the extreme scenario. The percentage of our method is 1.00 in the normal scenario and 0.94 in the extreme scenario. This means that the scheduling scheme generated by our method can satisfy 100% of normal scenarios and 94% of extreme scenarios, very close to the worst case based approach. The feasible scene numbers of the MC method and the opportunity constraint method are respectively 105 and 95, and are less than half of the methods. This means that the crew assembly solution generated by our method is much more robust than the other two methods.

The list of references used in the present invention is as follows:

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Claims

1. A method for analyzing load uncertainty of an electric power system is characterized by comprising the following steps:

5) Calculating whether each common sample and the center sample in the reconstructed historical load sample data have a corresponding economic dispatching scheme or not, and recording the score of each unit combination scheme reserved in the step 4); if the unit combination scheme has an economic scheduling solution under the common sample or the central sample, the fraction of the corresponding unit combination scheme is increased, the feasibility proportion of each unit combination scheme is calculated by using SI/NJ, wherein SI is the total fraction of each unit combination scheme, and NJ is the total number of the common samples and the central sample;

6) Selecting the central sample with the maximum local density in each cluster to replace all sample information in the cluster; the probability of fluctuation of the load of the power system is shown through the occurrence probability of the center sample of each cluster and the corresponding cluster; selecting a unit combination scheme with the maximum SI score, and calculating an economic dispatching result of each center sample according to the unit combination scheme; and finally, combining the calculation results of all the central samples through the occurrence probability of the corresponding clusters to obtain a final scheduling plan.

2. The method for analyzing uncertainty of load of electric power system according to claim 1, characterized in that in step 1), redundant information in historical load samples is removed by using principal component analysis method.

3. The method according to claim 1, wherein in step 2), the average density of the historical load samples in each cluster is calculated, and if the local density of a certain historical load sample is greater than the average density, the sample is identified as a core sample, otherwise, the sample is an edge sample, i.e., an extreme sample; the cluster center in the core sample is the center sample, and the others are the common samples.

4. The method according to claim 1, wherein in step 3), the historical load samples are reconstructed using the following equation

Wherein,

S _s for the s-th load scenario, N is the number of load scenarios, Λ _m ＝[e ₁ ,e ₂ ,......,e _m ]，e ₁ ,e ₂ ,……e _τ Is a covariance matrix Δ S ^T The feature vector matrix of (a) is,

5. the method for analyzing the load uncertainty of the power system as claimed in claim 1, wherein in the step 4), whether a unit combination scheme exists is judged by using the following unit combination models:

wherein, F _i (p _its ) Represents the coal-fired cost, SU, of the ith unit at the tth moment in the scene s _its Representing the startup cost of the ith unit at the tth moment under the scene s, NG representing the number of coal-fired units, NT representing the planned time scale, and p _its Represents the output of the ith coal-fired unit at the t moment under the scene s, PD _ts Representing the load value, R, at time t under scene s _i Represents the climbing upper limit, p, of the ith unit _min,i ,p _max,i Respectively representing the minimum and maximum output of the ith unit, I _its Representing the state of the unit i at the t-th moment in the scene s, X _on,i(t-1)s ,X _off,i(t-1)s Respectively representing the cumulative opening and closing time of the ith unit at the T-1 th moment under the scene s, T _on,i ,T _off,i Respectively representing the minimum startup and shutdown time required by the ith unit, wherein SF represents a system transfer factor matrix, K _p ,K _D Respectively representing unit and load node connection matrices, PL _max Representing the upper limit of the line flow; p _ts ,PD _ts Respectively representing the output of the coal-fired unit and the system load at the time t of the scene s.

6. The method for analyzing uncertainty of load in electric power system according to claim 5, wherein in step 6), the economic dispatch calculation is performed using the following formula:

where NS denotes the number of typical scenes, π _s Representing the probability of the occurrence of the s-th typical scene.