A rapid assessment method for provincial power balance margin considering source-load uncertainty and market mechanism

Abstract

The present invention belongs to the technical field of power system assessment, and specifically discloses a method for rapid assessment of provincial power balance margin taking into account source-load uncertainty and market mechanism. It includes: using non-parametric kernel density estimation to model the marginal distribution of source-load output forecast errors; performing correlation modeling and generating random samples for random samples generated based on a probability model; simultaneously obtaining two groups of corresponding random samples that are independent of each other and obey a standard normal distribution; constructing a provincial power balance margin assessment model, using the two groups of sample sets as inputs of a provincial power balance margin assessment deterministic model, and establishing a power balance margin proxy calculation model based on BASPC; using random samples as inputs of the BASPC proxy model to calculate the final provincial power balance margin; and quantifying the line congestion risk under the influence of source-load uncertainty through the system line load rate. The present invention can quickly and accurately assess the power balance margin and promptly discover the risk of line congestion within the province.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system evaluation, and specifically discloses a method for quickly evaluating provincial power balance margin taking into account source-load uncertainty and market mechanisms. Background Art

[0002] In recent years, with the rapid development of the new energy industry, the contradiction of "reverse distribution of source and load" in the power system has been further aggravated. Inter-provincial and inter-regional power transmission is the main way to resolve this contradiction.

[0003] In the electricity spot market, as the proportion of renewable energy among sellers and diverse load types among buyers increases, the resulting source-load uncertainty exacerbates risks in electricity prices and power balance within the market. This phenomenon is particularly prominent in interprovincial electricity markets encompassing multiple regions. The intraprovincial power balance margin is crucial information in the interprovincial electricity spot market. During the three-stage clearing process in the interprovincial electricity market, source-load uncertainty is first transmitted to the interprovincial region through the pre-cleared intraprovincial power balance margin. Subsequently, the interprovincial market feeds back inaccurate clearing results to the province for formal clearing. This indicates that source-load uncertainty, carried by the intraprovincial power balance margin, is repeatedly transmitted across the two-tier market, exacerbating risks to the safe and economic operation of the electricity spot market. Therefore, it is necessary to study the impact of source-load uncertainty on the intraprovincial power balance margin.

[0004] Currently, in the context of interprovincial electricity spot trading, the power balance margin is presented at each interconnected node in the form of pre-planned delivery / receipt volume during official provincial clearing, and participates in the provincial power balance. During this period, intra-provincial line congestion may occur, posing a threat to the safe and stable operation of the provincial power grid. Therefore, accurately assessing the power balance margin and mitigating these risks are crucial for the safe and stable operation of both intra-provincial and inter-provincial markets.

[0005] The Polynomial Chaos Expansion (PCE) model, a typical proxy model, has been widely used in probabilistic optimal power flow for power systems. Its core concept is to use a set of orthogonal polynomials to approximate the original deterministic model, which relies on complex computations, thereby achieving efficient estimation of the output response. However, traditional PCE models can lead to the curse of dimensionality as the number of variables and the order of the expansion terms increase. Summary of the Invention

[0006] The present invention aims to provide a method for rapidly evaluating the power balance margin within a province, taking into account source-load uncertainty and market mechanisms. This method solves the technical problem that the traditional PCE model will cause a dimensionality disaster as the dimension of the variables and the order of the expanded terms increase, and rapidly and accurately evaluates the power balance margin and promptly discovers the risk of line congestion within the province.

[0007] The method for rapidly assessing the provincial power balance margin considering source-load uncertainty and market mechanisms in the present invention comprises the following steps:

[0008] Step S1: Model the marginal distribution of source-load output prediction errors using nonparametric kernel density estimation;

[0009] Step S2: performing correlation modeling on the random samples generated based on the probability model and generating random samples;

[0010] The Spearman rank correlation coefficient matrix method is used to characterize the correlation between variables, and two groups of random samples are obtained based on the probability model. One group is a l×n-dimensional random sample X=[x1,…,x l ] T , the other group is l×N E X-dimensional experimental design sample E =[x E1 ,…,x El ] T , where N E Usually much smaller than n; at the same time, obtain the corresponding independent l×n dimensional random samples Q=[q1,…q l ] T and l×N E dimensional random sample Q E =[q E1 ,…,q El ] T ;

[0011] Step S3: Taking the contact node as the starting point, the provincial power balance margin assessment model is constructed in combination with the pre-clearing mechanism. E As the input of the provincial power balance margin assessment deterministic model, the provincial power balance margin σ=[σ1,…,σ n ] and σ E =[σ E1 ,…,σ ENE ];

[0012] Step S4: Use the generated experimental design sample Q E And the corresponding output σ E Establish a power balance margin proxy calculation model based on BASPC;

[0013] Step S5: Take the l×n-dimensional independent random sample Q as the input of the BASPC agent model and calculate the final provincial power balance margin σ B =[σ B1 ,…,σ Bn ];

[0014] Step S6: Based on the above-mentioned provincial power balance margin calculation model, the blocking risk of the line under the influence of source-load uncertainty is quantified by the system line load rate.

[0015] This paper incorporates pre-planned power transmission and reception into traditional pre-clearing models, proposing a model for assessing the provincial power balance margin that considers source-load uncertainty and the impact of market mechanisms. This model can improve the accuracy of provincial power balance margin assessments. Furthermore, this paper applies the BASPC expansion method to the electricity spot market for the first time, establishing a proxy assessment model for the provincial power balance margin that considers source-load uncertainty based on BASPC, significantly improving the efficiency of power balance margin assessments. Furthermore, based on the combined allocation of contact nodes, a trading node partitioning method with minimal congestion risk can be obtained, which helps reduce the risk of line congestion to normal market operation. These findings have been validated in case studies.

[0016] In summary, the beneficial effects of the present invention are:

[0017] (1) A method for evaluating the provincial power balance margin considering source-load uncertainty and market mechanism is proposed. The proposed method can select the optimal division method of transaction nodes according to the provincial congestion risk under the combination allocation of connection nodes, and realize the accurate evaluation of the provincial power balance margin under the optimal division method.

[0018] (2) The BASPC expansion method was introduced for the first time in the assessment of power balance margin within the power market, which greatly improved the efficiency of power balance margin assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 .It is a flow chart of a method for rapid assessment of provincial power balance margin taking into account source-load uncertainty and market mechanism in an embodiment of the present invention.

[0020] Figure 2 This is a flow chart of the provincial power balance margin assessment based on BASPC in an embodiment of the present invention.

[0021] Figure 3 . This is a structural diagram of the improved IEEE RTS96 system in an embodiment of the present invention.

[0022] Figure 4 This is a power generation side quotation curve diagram in an embodiment of the present invention.

[0023] Figure 5 Schematic diagram of the provincial power balance margin result in an embodiment of the present invention.

[0024] Figure 6 Schematic diagram of the probability distribution of the power balance margin of the contact node at 16:00 in an embodiment of the present invention.

[0025] Figure 7 Schematic diagram of probability density distribution of power balance margin under different evaluation models in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In this example, the rapid assessment method of provincial power balance margin considering source-load uncertainty and market mechanism is as follows: Figure 1 As shown, the calculation steps are as follows:

[0027] Step S1: Use non-parametric kernel density estimation to model the marginal distribution of source-load output prediction errors.

[0028] Step S2: perform correlation modeling and random sample generation on the random samples generated based on the probability model; use the Spearman rank correlation coefficient matrix method to characterize the correlation between variables, and sample based on the probability model to obtain two groups of random samples, one of which is a l×n-dimensional random sample X=[x1,…,x l ] T , the other group is l×N E X-dimensional experimental design sample E =[x E1 ,…,x El ] T , where N E Usually much smaller than n;

[0029] In this process, the corresponding l×n dimensional random samples Q=[q1,…q l ] T and l×N E dimensional random sample Q E =[q E1 ,…,q El ] T .

[0030] Step S3: Taking the contact node as the starting point, the provincial power balance margin assessment model is constructed in combination with the pre-clearing mechanism. E As the input of the provincial power balance margin assessment deterministic model, the provincial power balance margin σ=[σ1,…,σ n ] and σ E =[σ E1 ,…,σ ENE ].

[0031] Step S4: Use the generated experimental design sample Q E And the corresponding output σ E Establish a power balance margin agent calculation model based on BASPC.

[0032] Step S5: Take the l×n-dimensional independent random sample Q as the input of the BASPC agent model and calculate the final provincial power balance margin σ B =[σ B1 ,…,σ Bn ].

[0033] Step S6: Based on the above-mentioned provincial power balance margin calculation model, the blocking risk of the line under the influence of source-load uncertainty is quantified by the system line load rate.

[0034] There are many sources of uncertainty in the power system. To obtain the required number of samples, based on measured data, in step 1 of this example, nonparametric kernel density estimation is used to model the marginal distribution of the source-load output forecast error. The formula for calculating the uncertain source output forecast error is as follows:

[0035]

[0036] Where: ΔP U,t is the power prediction error of the uncertain source at time t; and P U,t are the predicted and measured values ​​of the uncertain source power at time t. Let f(x) be the random variable x=[x1,…x n ], and its kernel density estimate is:

[0037]

[0038] Where: w is the bandwidth; K(·) is the kernel function; n is the number of samples.

[0039] In reality, there is correlation between variables such as wind power and load. Since it is impossible to directly sample samples with correlation, in step 2 of this example, the Spearman rank correlation coefficient of the measured data is first extracted; then, random samples that are independent of each other and follow a standard normal distribution are generated; finally, based on the probability transformation principle such as Cholesky decomposition, these samples are converted into random samples that have correlation and follow the original distribution. The specific principles are as follows:

[0040] For the l×n dimensional random sample matrix X=[x1,…x l ] T , its correlation coefficient matrix C s,x for:

[0041]

[0042] Where, ρ s,xij Represents the Spearman rank correlation coefficient between the i-th dimension variable and the j-th dimension variable in the original domain.

[0043] When the marginal distribution of the random variable changes, the rank correlation coefficient remains unchanged, that is, the Spearman rank correlation coefficient in the standard normal domain is equal to the correlation coefficient in the original domain, and the relationship between the Pearson correlation coefficient and the Spearman rank correlation coefficient in the standard normal domain is as shown in formula (4):

[0044]

[0045] Where, ρ zij and ρ s,zij Represents the Pearson correlation coefficient matrix C under the standard normal domain z and the Spearman rank correlation coefficient matrix C s,z The element in the i-th row and j-th dimension of .

[0046] Based on the Monte Carlo simulation (MCS) method, an independent standard normal sample Q of dimension l×n is generated. l ] T Q can be converted into a standard normal random sample matrix Z = [z1,…z l ] T :

[0047] Z=LQ (5)

[0048] In the formula, L can be obtained by the correlation coefficient matrix C z Perform Cholesky decomposition to obtain:

[0049] C z =LL Τ (6)

[0050] For the k-th dimension random variable, according to the equal probability transformation principle shown in formula (7), a random sample that satisfies the original domain distribution can be obtained:

[0051]

[0052] Where Φ(·) represents the standard normal cumulative distribution function; F k -1 is the inverse function of the original cumulative distribution function F.

[0053] In inter-provincial electricity spot market transactions, the province is generally used as the smallest trading unit. However, when severe line congestion occurs frequently within a province, two or more trading nodes can be defined. The intra-provincial power balance margin in this example is a general term, which can be expressed as the power balance margin of one or more trading nodes within the province. The traditional pre-clearing model (collectively referred to as the traditional model in this example) only considers the source-load balance constraints within the province when solving, and does not consider the external transmission of the connecting node. As a result, the congestion of some lines within the province that appears when solving the model is not equivalent to the line congestion when the external transmission of the connecting node is considered during the formal clearing. In this regard, this example proposes a provincial power balance margin assessment model that takes the external transmission of the connecting node into account during pre-clearing.

[0054] Typically, a trading node contains at least one interconnection node, and the evaluation of the interconnection node's power balance margin is the basis for evaluating the power balance margin of the trading node. Based on the above situation, this example sets the interconnection node's power balance margin as the decision variable of the optimization model, which is constrained by the available transmission capacity. When solving the model, the interconnection nodes of the sending and receiving provinces can be equivalent to load nodes and generator nodes, respectively. The objective function of the proposed optimization model is to maximize the economic benefits of the province:

[0055]

[0056] Where: C c,t is the inter-provincial profit coefficient of contact node c in transaction period t; c,t is the power balance margin of the connecting node during trading period t (positive for the sending end and negative for the receiving end). Compared with the traditional pre-clearing model, the constraints of the model proposed in this example are changed as follows:

[0057]

[0058] Where: P lt,h is the planned power of tie line h in the medium and long-term contract (outflow is negative, inflow is positive); N c is the sum of all contact nodes in the region; is the available transmission capacity of contact node c during transaction period t.

[0059] Through the above optimization model, the two sample sets X and X E As the input of the provincial power balance margin assessment deterministic model, the required provincial power balance margin σ=[σ1,…,σ l ] and σ E =[σ E1 ,…,σ El ], which is the sum of the power balance margins of all connected nodes.

[0060] If m input independent random variables ξ=[ξ1,ξ2,...,ξm There is a nonlinear functional relationship Y = f(ξ) between ] and the output Y. According to the chaotic polynomial expansion theory, it can be expanded and approximated by a set of orthogonal polynomials:

[0061]

[0062] Where: f(·) is the original model; g(·) is the proxy model; u is the different polynomial basis functions Ψ u Index of (ξ); is the set of truncation solutions; γ u is the expansion coefficient. Multivariate polynomial basis function Ψ u (ξ) is composed of the tensor product of each unary basis function:

[0063]

[0064] Where: is a random variable ξ v The corresponding u v The orthogonal polynomials of different orders are used. The corresponding orthogonal polynomial basis functions need to be selected for the marginal distribution types of different random variables. Reference [1] lists the basis functions corresponding to common probability distributions. When formula (12) is expanded and calculated, the finite terms of the model will be truncated according to the truncation parameter p. After truncation, the number of expansion terms of the approximate model is R. m,p for:

[0065]

[0066] The above truncation is called the standard truncation scheme, denoted by Θ m,p ={u∈ m :||u||1≤p}, where ||·||1 is the 1-norm. It can be seen that the number of expanded terms is affected by the number of input variables and the truncation parameter. The larger the truncation parameter p, the higher the accuracy of the model, but the number of expanded terms will increase, and the computational complexity will also increase. When the truncation standard parameter p = 2, the polynomial expansion of the output variable is:

[0067]

[0068] Where: Ψ1(ξ u ) and Ψ2(ξ u ,ξ v ) are variables ξ u The corresponding first-order orthogonal polynomial and variable ξ u ,ξ v The corresponding second-order orthogonal polynomials.

[0069] Therefore, in step 4 of this paper, the provincial power balance margin assessment method based on the BASPC expansion method is adopted.

[0070] This method introduces the BASPC expansion method to achieve rapid evaluation of the provincial power balance margin. The evaluation process is as follows: Figure 2 shown.

[0071] It can be seen that there are two main steps in constructing the BASPC expansion model: first, a set of experimental design (ED) sample sets is generated by random sampling; second, according to the set truncation parameter range [p min ,p max ], and a sparse expansion inner loop strategy based on hyperbolic truncation scheme and minimum angle regression to establish a BASPC expansion model. min ,p max ], the basis function set constructed based on the hyperbolic truncation scheme is:

[0072]

[0073] Where: ||·|| q is the q-norm. When q<1, the high-order interaction terms with small contributions are eliminated, and the smaller q is, the more terms are eliminated. When q=1, it is the standard truncation scheme. Compared with the standard truncation scheme, hyperbolic truncation can obtain a sparse set of basis functions. For the expansion coefficient γ u The estimation of is usually done using the least squares method:

[0074]

[0075] Where: E The Eth sample designed for the experiment; N E is the total number of experimental design samples; γ=[γ0,...,γ W ] represents the polynomial coefficient, W is the total number of terms under the hyperbolic truncation scheme; J(χ E )=[Ψ0(χ E ),…,Ψ W (χ E )] is the sample point χ E The corresponding orthogonal polynomial matrix, the solution of the expansion coefficient can be obtained according to the following formula:

[0076]

[0077] Where: γ represents the output sample set obtained by bringing the experimental design sample set into the original model. In order to screen the most relevant expansion items, a penalty term is introduced based on formula (17):

[0078]

[0079] Where: λ is the penalty factor; in this example, the least angle regression (LAR) method is used to solve it.

[0080] For the selection of truncation parameter p, this example uses the leave-one-out (LOO) cross-validation error e LOO To determine the most appropriate p-value, we have:

[0081]

[0082] Where: g (E) (·) is the PCE model under the new sample set formed after deleting the E-th sample.

[0083] Based on this method, the optimal value p* can be selected:

[0084]

[0085] The optimal sparse basis function set corresponding to p* and the corresponding coefficients constitute the BASPC model. The specific steps of the hyperbolic truncation scheme, minimum angle regression, and LOO cross-validation are detailed in the literature [2].

[0086] When severe congestion frequently occurs within a province, multiple transaction nodes need to be divided. Each transaction node contains at least one contact node. If allocation is based solely on the combination of contact nodes without considering the division of other nodes, there are a total of Z ways to allocate transaction nodes:

[0087]

[0088] Where: N b is the maximum number of transaction nodes, that is, the total number of contact nodes; b is the number of transaction nodes; S is the second kind of Stirling number.

[0089] In this example, the system line load factor is used to quantify the line congestion risk under the influence of source load uncertainty. This indicator is defined as the average of all line load factors in the entire power system:

[0090]

[0091] Where S L,max is the maximum capacity of line L; S L is the branch power of line L; N L is the total number of branches.

[0092] In this example, the feasibility of the proposed model is verified by using the improved IEEE RTS96 system [3]. The system is composed of three areas and five interconnected lines. Its network structure is as follows: Figure 3As shown. Set area A as the sending area, area C as the transmission area, and area B as the receiving area. Area A contains four connection nodes:

[0093] At nodes 121, 123, 113, and 107, Area A's conventional units have a total installed capacity of 3,018 MW, with a maximum load of 2,850 MW. Five renewable energy power plants have been introduced in Area A, including three photovoltaic power plants at nodes 118, 121, and 122, and two wind farms at nodes 101 and 102. Their installed capacity accounts for 52.02% of the total conventional unit capacity.

[0094] The composition of uncertain sources varies in different time periods. In this example, the time scale is divided into daytime and nighttime. The daytime period is 07:00-19:00. The uncertain sources in the daytime period include photovoltaic power, wind power, and load, while the uncertain sources in the nighttime period are only wind power and load. In addition, since this example only considers the power generation side for quotation, the corresponding "electricity quantity-electricity price" curve is as follows: Figure 4 shown.

[0095] According to statistics, the maximum total load output of Belgium in 2022 is 12.7 million kilowatts, which is close to the total load output of Qinghai Province. Therefore, this example uses the publicly available Belgian source load output data to simulate the source load output of a province, specifically including the measured and predicted output data of new energy stations and total load. The power data of the new energy stations are shown in Table 1; the load data uses the Belgian total load data scaled by the ratio (the ratio of the maximum total load of Belgium to the total load of the example system). The data period is from December 31, 2022 to September 30, 2023. Referring to the "electricity-price" curve in reference [4], this example sets 9 quotation curves, and the specific quotation and quotation data are shown in Tables 2 and 3. The time scale in this example is 24 trading periods in a day in the day-ahead electricity spot market. The simulation experiment was implemented in the Matlab R2019a environment, and the establishment of the BASPC agent model was completed with the help of the UQLab V2.0 toolbox [2].

[0096] Table 1. New energy station power data

[0097]

[0098] Table 2. New energy station power data

[0099]

[0100] Table 3. New energy station power data

[0101]

[0102]

[0103] The frequency histogram of the measured data is used as a reference for accuracy. The Frequency Histogram Similarity Index (FHSI) [5] is used to verify the accuracy of the probability density of the generated random samples. The value range of FHSI is [0, 1]. The closer it is to 1, the better the effect. Table 4 shows the FHSI index of six random samples.

[0104] Table 4 FHSI index of random samples

[0105]

[0106] Table 4 shows that the FHSI index for all six random samples is above 0.97. This indicates that the generated random samples fully preserve the marginal distribution characteristics of the measured data. Furthermore, the experimentally obtained mean absolute error (MAE) of the correlation coefficient matrix between the generated random samples and the measured data is only 0.0015, validating the accuracy of the uncertainty model established in this example.

[0107] Figure 5 The following is a schematic diagram of the simulated provincial power balance margin results, where:

[0108] Figure 5 (a) The intra-day (24-hour) power balance margin calculated based on the proposed model in this example shows a gradual increase from 1:00 to 6:00, 9:00 to 16:00, and 21:00 to midnight. The increase from 9:00 to 16:00 is attributed to high photovoltaic power generation, while the changes in the power balance margin in the other two periods are dominated by system load. Conversely, as the power load increases, the provincial power balance margin decreases from 6:00 to 9:00, and due to the time correlation of photovoltaic power generation, the power balance margin decreases rapidly from 17:00 to 21:00. In general, the provincial power balance margin is positively correlated with the system's remaining generation capacity.

[0109] Figure 5 (b) is the probability distribution FHSI index of the power balance margin within the province of the two models. The changing trend of the FHSI index is opposite to the changing trend of the power balance margin. The larger the power balance margin, the greater the difference in the calculation results of the two models. Figure 5 (c) is the probability distribution of the provincial power balance margin of the two models at two time points, as shown in Figure 5As shown in (c), at 21:00 when the mean margin is the smallest, the margin frequency histograms of the two models are almost completely overlapped, while at 16:00 when the mean margin is the largest, there is a significant difference. When the surplus power generation capacity within the province is small, the two models have similar mechanisms and the calculation results of the power balance margin are slightly different; when the surplus power generation capacity within the province is large, the calculation results of the traditional model are optimistic because the influence of network transmission constraints and economic efficiency is not considered. The proposed model uses the power balance margin as the decision variable, takes into account the influence of the quotation and grid topology constraints, and the calculation results are more realistic. Therefore, the proposed model is more accurate in evaluating the power balance margin under the influence of source and load uncertainty. For provinces with large power balance margins, such as Northwest China with a large amount of renewable energy, the proposed model in this example is more suitable.

[0110] In addition to the calculation error in the total power balance margin, the traditional model also has the defect of being unable to obtain the power balance margin of the interconnection node. In the model proposed in this example, the power balance margin within the province is the sum of the power balance margins of all interconnection nodes. For each interconnection node, its power balance margin has a one-to-one correspondence under the uncertainty scenario, that is, it is affected by the interactivity of the physical model. Taking 16:00 as an example, the probability distribution of the power balance margin of each interconnection node calculated based on the proposed model is as follows: Figure 6 As shown in Figure 2, the significant differences reveal that the proposed model is sensitive to the intra-provincial market mechanism, indicating that its calculation results are more in line with reality.

[0111] In addition to accuracy requirements, the efficiency of power balance margin assessment in the day-ahead power spot market is equally important. As the number and types of source-load uncertainties increase, the MCS-based power balance margin assessment model (original model) is difficult to meet the power balance margin assessment speed requirements. To this end, a proxy model based on BASPC expansion is constructed in this example. Table 5 shows the accuracy and time consumption of the proxy model and the original model under different experimental samples. E represents the number of experimental samples used to construct the surrogate model; T1 and T2 represent the surrogate model building time and the surrogate model-based evaluation time, respectively. Furthermore, the table shows the calculation results at 4:00 PM. Unless otherwise specified, subsequent experimental results will analyze the same time.

[0112] Table 5 Statistical results of provincial power balance margin under different evaluation models

[0113]

[0114] As shown in Table 5, different N E The average relative deviation between the lower surrogate model and the original model is within 1.6%, indicating that it has a high approximation accuracy. LOO With N EThe reason is that more training samples can provide more accurate probability information to improve the accuracy of the agent model, but it also means that more training time is required, as shown in Table T1. In this example, the power balance margin assessment (pre-clearing) of the day-ahead spot market needs to be completed within one hour. Considering the requirements of both accuracy and efficiency, the experimental sample N is E The power balance margin probability results calculated by the BASPC model based on this setting are shown in Table 6.

[0115] Table 6 Statistical results of interconnection node power balance margin under different evaluation models

[0116]

[0117]

[0118] The FHSI values ​​for the interconnected node power balance margins calculated by both evaluation models in Table 6 are both above 0.9, indicating highly similar probabilistic results. Furthermore, the BASPC proxy model takes only 133.63 seconds, only 3.22% of the original model, demonstrating its superior evaluation efficiency. Figure 7 The probability density distribution of the power balance margin of the connecting node 113 and area A is shown. It can be seen that the probability density graphs under the two evaluation models are almost overlapping, which once again verifies the accuracy of the proposed model.

[0119] This example uses 15 different trading node allocation methods. Four scenarios are analyzed at 4:00 PM. The trading node allocation for each of the four scenarios is shown. Lines marked in red indicate that the power of the branch has reached the line capacity limit, indicating overload. Trading nodes are allocated based on overloaded lines as much as possible. Scenario 1 includes four trading nodes: 121, 123, 113, and 107; Scenario 2 includes three trading nodes: 121-123, 113, and 107; Scenario 3 includes two trading nodes: 121-123 and 113-107; and Scenario 4 includes one trading node: 121-123-113-107.

[0120] References

[0121] [1]Sun Xin,Tu Qingrui,Chen Jinfu.Probabilistic load flow calculationbased on sparse polynomial chaosexpansion[J].IET Generation,Transmission&Distribution,2018,11(12):2735-2744.

[0122] [2]MARELLI S,SUDRET B.UQLab: a framework for uncertainty quantification in MATLAB[C] / / 2ndInternational Conference on Vulnerability,Risk Analysis and Management.Liverpool:ICVRAM,2014.

[0123] [3] Zhang Runfan, Ling Xiaobo, Ren Xinyi, et al. Two-layer clearing model of inter-provincial and intra-provincial spot markets based on multiple trading methods [J / OL]. Power System Automation

[0124] Chemical, 1-25[2024-04-08].

[0125] [4] Jiang Nan. Research on joint clearing mechanism of multi-regional day-ahead power market[D]. North China Electric Power University (Beijing), 2020.

[0126] [5]X.Lin,S.Peng,J.Tang,et al.Regional Sensitivity Analysis forMaximum Static Transfer Capability ofPower Systems by Dimension-AdaptiveSparse Grid Interpolation[J].IEEE Transactions on Power Systems,

[0127] 2024,39(1):1095-1110.

Claims

1. A rapid assessment method for provincial power balance margin considering source-load uncertainty and market mechanism, characterized by: The following steps are involved: Step S1: Model the marginal distribution of source-load output prediction errors using nonparametric kernel density estimation; Step S2: performing correlation modeling on the random samples generated based on the probability model and generating random samples; The Spearman rank correlation coefficient matrix method is used to characterize the correlation between variables, and two groups of random samples are obtained based on the probability model. One group is a l×n-dimensional random sample X=[x1,…,x l ] T , the other group is l×N E X-dimensional experimental design sample E =[x E1 ,…,x El ] T , where N E Usually much smaller than n; at the same time, obtain the corresponding independent l×n dimensional random samples Q=[q1,…q l ] T and l×N E dimensional random sample Q E =[q E1 ,…,q El ] T ; Step S3: Taking the contact node as the starting point, the provincial power balance margin assessment model is constructed in combination with the pre-clearing mechanism. E As the input of the provincial power balance margin assessment deterministic model, the provincial power balance margin σ=[σ1,…,σ n ] and σ E =[σ E1 ,…,σ ENE ]; Step S4: Use the generated experimental design sample Q E And the corresponding output σ E Establish a power balance margin proxy calculation model based on BASPC; Step S5: Take the l×n-dimensional independent random sample Q as the input of the BASPC agent model and calculate the final provincial power balance margin σ B =[σ B1 ,…,σ Bn ]; Step S6: Based on the above-mentioned provincial power balance margin calculation model, the blocking risk of the line under the influence of source-load uncertainty is quantified by the system line load rate.

2. The method according to claim 1, characterized in that Step S1 specifically includes: The marginal distribution of the source-load output forecast error is modeled using nonparametric kernel density estimation. The calculation formula for the uncertain source output forecast error is as follows: Where: ΔP U,t is the power prediction error of the uncertain source at time t; and P U,t are the predicted value and measured value of the uncertain source power at time t respectively; Let f(x) be a random variable x=[x1,…x n ], and its kernel density estimate is: Where: w is the bandwidth; K(·) is the kernel function; n is the number of samples.

3. The method according to claim 2, characterized in that Step S2 specifically includes: Calculate the Spearman rank correlation coefficient of the measured data to form the correlation coefficient matrix of the random sample matrix; Furthermore, it generates random samples that are independent of each other and obey the standard normal distribution, and converts them into random samples that are correlated and obey the original distribution based on probability transformation principles such as Cholesky decomposition.

4. The method according to claim 3, characterized in that In step S2: For the l×n dimensional random sample matrix X=[x1,…x l ] T , its correlation coefficient matrix C s,x for: Where, ρ s,xij represents the Spearman rank correlation coefficient between the i-th dimension variable and the j-th dimension variable in the original domain; The relationship between the Pearson correlation coefficient and the Spearman rank correlation coefficient under the standard normal domain is established as follows: Where, ρ zij and ρ s,zij Represents the Pearson correlation coefficient matrix C under the standard normal domain z and the Spearman rank correlation coefficient matrix C s,z The element of row i and dimension j; Generate l×n-dimensional independent standard normal samples Q=[q1,…q l ] T , convert Q into a standard normal random sample matrix Z=[z1,…z l ] T as follows: Z=LQ (5) In the formula, L is obtained by the correlation coefficient matrix C z Perform Cholesky decomposition and we get: C z =LL Τ (6) For the k-th dimension random variable, according to the equal probability transformation principle shown in the following formula, a random sample that satisfies the original domain distribution is obtained: Where Φ(·) represents the standard normal cumulative distribution function; F-1k is the inverse function of the original cumulative distribution function F.

5. The method according to claim 1, wherein Step S3 specifically includes: The power balance margin of the tie node is set as the decision variable of the optimization model, which is constrained by the available transmission capacity; When solving the optimization model, the connection nodes of the sending and receiving provinces are equivalent to load nodes and generator nodes respectively. The objective function of the optimization model is to maximize the economic benefits of the province as follows: Where: C c,t is the inter-provincial profit coefficient of contact node c in transaction period t; c,t is the power balance margin of the contact node in the trading period t, and the optimization model constraints are as follows: Where: P lt,h is the planned power of tie line h in the medium and long-term contract, outflow is negative and inflow is positive; N c is the sum of all contact nodes in the region; is the available transmission capacity of contact node c during transaction period t; Through the above optimization model, the two sample sets X and X E As the input of the provincial power balance margin assessment deterministic model, the required provincial power balance margin σ=[σ1,…,σ l ] and σ E =[σ E1 ,…,σ El ].

6. The method according to claim 5, characterized in that Step S4 specifically includes: Step 4.1: Establish the model approximation strategy as follows: If m input independent random variables ξ=[ξ1,ξ2,...,ξ m There is a nonlinear functional relationship Y = f(ξ) between ] and the output Y, which can be approximated as the expansion and approximation of a set of orthogonal polynomials: Where: f(·) is the original model; g(·) is the proxy model; u is the different polynomial basis functions Ψ u Index of (ξ); is the set of truncation solutions; γ u is the expansion coefficient, the multivariate polynomial basis function Ψ u (ξ) is composed of the tensor product of each unary basis function: Where: is a random variable ξ v The corresponding u v The orthogonal polynomials of different orders should be selected, and the corresponding orthogonal polynomial basis functions should be selected for the marginal distribution types of different random variables; The model is truncated according to the truncation parameter p, and the number of expanded terms of the approximate model after truncation is R m,p for: The above truncation is called the standard truncation scheme, denoted by Θ m,p ={u∈ m :||u||1≤p}, where ||·||1 is the 1-norm; when the truncation standard parameter p=2, the polynomial expansion of the output variable is: Where: Ψ1(ξ u ) and Ψ2(ξ u ,ξ v ) are variables ξ u The corresponding first-order orthogonal polynomial and variable ξ u ,ξ v The corresponding second-order orthogonal polynomials; Step 4.2: Construct the BASPC expansion model, including: First, obtain the experimental design sample set; Secondly, according to the specified cutoff parameter range [p min ,p max ] and a sparse expansion inner loop strategy based on hyperbolic truncation scheme and minimum angle regression to establish the BASPC expansion model; Among them, for the truncation parameter p∈[p min ,p max ], the basis function set constructed based on the hyperbolic truncation scheme is: Where: ∥·∥ q is the q-norm; For the expansion coefficient γ u The estimation of is done using a minimization model: Where: E The Eth sample designed for the experiment; N E is the total number of experimental design samples; γ=[γ0,...,γ W ] represents the polynomial coefficient, W is the total number of terms under the hyperbolic truncation scheme; J(χ E )=[Ψ0(χ E ),…,Ψ W (χ E )] is the sample point χ E The corresponding orthogonal polynomial matrix; λ is the penalty factor; The above optimization model is solved by the minimum angle regression method, and the error e is cross-validated by the leave-one-out method. LOO Determine the most appropriate p-value, there are; Where: g (E) (·) is the PCE model formed under the new sample set after deleting the Eth sample, and the optimal value p is selected. * : p * The corresponding optimal sparse basis function set and corresponding coefficients constitute the BASPC model.

7. The method according to claim 1, characterized in that Step S6 specifically includes: When severe congestion frequently occurs within a province, multiple transaction nodes are divided. Each transaction node contains at least one contact node. The nodes are allocated only according to the combination of contact nodes. There are Z types of transaction node allocation methods: Where: N b is the maximum number of transaction nodes, that is, the total number of contact nodes; b is the number of transaction nodes; S is the second kind of Stirling number; The blocking risk of lines under the influence of source load uncertainty is quantified by the system line load factor, which is defined as the average of all line load factors in the entire power system: Where S L,max is the maximum capacity of line L; S L is the branch power of line L; N L is the total number of branches.

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