A power grid limit uncertainty evaluation method based on new energy power confidence

Abstract

The application discloses a power grid limit uncertainty evaluation method based on new energy power confidence, and belongs to the field of power system uncertainty analysis. The method firstly utilizes quantile regression and shape-preserving prediction to construct a new energy power marginal confidence interval with limited sample coverage guarantee from historical prediction errors; secondly, a t-Copula function is used to fit the space-time correlation of multi-station output error to generate a multi-dimensional joint confidence region; then, based on the power transfer distribution factor, a linear sensitivity matrix of new energy output fluctuation to cross-section power flow is established; finally, the multi-dimensional confidence region and the sensitivity matrix are subjected to closed interval operation to quickly obtain the cross-section limit transmission capacity interval under the specified confidence level. The application avoids the error of parameter distribution assumption, has sub-millisecond calculation speed and strict statistical guarantee, and provides a transmission capacity uncertainty quantitative boundary that can be directly used for risk decision-making for dispatching operation.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, specifically to a method and apparatus for assessing the ultimate uncertainty of power grids based on the confidence level of new energy power. It is applicable to the quantification and online assessment of the ultimate transmission capacity of cross-regional transmission sections in power systems with a high proportion of new energy. Background Technology

[0002] With the large-scale integration of new energy sources such as wind and solar power into the power grid, the operation mode of the power system is becoming increasingly complex. Accurate assessment of the maximum transmission capacity (MTC) at different sections has become one of the key technical challenges for the safe and stable operation of the power grid. The MTC at a given section directly determines the physical upper limit of power exchange between regions and is the core basis for dispatching operations, market transactions, and transmission planning. However, the strong randomness and volatility of new energy output pose a serious challenge to traditional MTC calculation methods based on deterministic power flow.

[0003] In existing technologies, cross-sectional MTC evaluation mainly suffers from the following problems: First, deterministic methods cannot reflect the stochastic nature of renewable energy output. Traditional cross-sectional MTC assessments are based on deterministic optimal power flow or continuous power flow, gradually increasing transmission power until safety constraints are triggered based on a specific operating mode. These methods typically employ worst-case scenarios or fixed margins, failing to reflect the probabilistic characteristics of renewable energy output. This results in overly conservative assessments, leading to underutilization of transmission channels, and the lack of statistical basis for setting conservative margins.

[0004] Second, probabilistic methods struggle to directly output confidence intervals for scheduling decisions. Probabilistic assessment methods based on Monte Carlo simulations solve for the statistical distribution of MTC through extensive random sampling, achieving high accuracy but incurring enormous computational costs, making them unsuitable for real-time or online applications. While semi-analytical surrogate model methods such as Latin hypercube sampling, point estimation, and multinomial chaotic expansion effectively reduce computation, these methods primarily focus on the probabilistic distribution characteristics of MTC, rarely providing MTC assessment intervals with guaranteed confidence levels. This lack of intuitive risk quantification in practical scheduling decisions makes them difficult for schedulers to directly apply to risk management.

[0005] Third, there is a lack of statistical correlation between the intervals obtained by interval optimization methods and the confidence levels. Existing interval optimization methods only require information on the upper and lower bounds of renewable energy output, decomposing the original problem into optimistic and pessimistic sub-problems to obtain the possible range of MTC. These methods have simple models and low data requirements, but the obtained intervals are relatively broad, and there is a lack of clear statistical correlation between the interval boundaries and the confidence levels. The interval width cannot quantify the corresponding risk and is difficult to meet specific reliability requirements.

[0006] Fourth, existing methods do not adequately consider the spatiotemporal correlation structure of renewable energy output. From the perspective of uncertainty source modeling, existing literature shows significant differences in how it characterizes the uncertainty of renewable energy output. Methods based on parametric modeling such as Weibull and Beta distributions rely on assumptions, leading to large evaluation biases when the actual distribution does not match the assumptions. More importantly, the prediction errors of multiple renewable energy power plants in the actual power grid exhibit significant spatiotemporal correlations, making the independent and identically distributed assumption difficult to hold. However, existing MTC uncertainty assessment studies rarely systematically utilize historical prediction error data to construct nonparametric confidence intervals, and they also lack effective modeling and utilization of the spatiotemporal correlation structure of multiple power plants, resulting in a lack of rigorous statistical verification to ensure the coverage of confidence intervals.

[0007] Fifth, there is a lack of efficient uncertainty assessment methods in multi-section coupling scenarios. Real-world power grids often present scenarios where multiple critical sections are simultaneously constrained, and power flow coupling exists between these sections. Existing methods suffer from high computational complexity and low efficiency when facing multi-section, multi-time-period assessment needs, making it difficult to achieve rapid joint assessment of MTC confidence intervals for sections with coupling constraints.

[0008] In summary, there is an urgent need for a method to assess the uncertainty of the ultimate transmission capacity of the power grid, which can construct a statistically guaranteed cross-sectional MTC confidence interval, fully consider the spatiotemporal correlation of new energy output, and has computational efficiency that meets the requirements of online applications. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method and apparatus for assessing the ultimate uncertainty of power grids based on the confidence level of renewable energy power. This method can directly start from historical prediction error data to construct a confidence interval for the ultimate transmission capacity of a section with strict coverage statistical guarantees. It fully considers the spatiotemporal correlation structure between multiple renewable energy power plants and achieves sub-millisecond-level rapid assessment through analytical linear mapping and interval operations. This provides a quantitative boundary for transmission capacity uncertainty that can be directly used for risk decision-making in scheduling operations.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: Step S1: Construct the marginal confidence interval.

[0011] Historical predicted power and historical actual output data of multiple renewable energy power plants in the power grid are obtained to construct a prediction error dataset. Then, a nonparametric statistical method is used to construct the marginal confidence interval of the output prediction error of each renewable energy power plant under a preset confidence level, and obtain the upper and lower bounds of the prediction error for each power plant.

[0012] The new energy power stations include wind farms and photovoltaic power stations. For those containing... The system of a new energy power station Record the time of the first site The predicted power for the day is Actual output is The prediction error is then defined as:

[0013] The prediction errors of all stations at all times are compiled into a dataset. ,in This represents the total number of time periods in the historical data. The dataset is divided into three parts: a training set, a calibration set, and a test set.

[0014] At the preset credit level The specific implementation process is as follows: First, initial intervals are constructed using quantile regression. For the significance level... Define the lower quantile and upper quantile Two conditional quantile models are fitted to each station on the training set, and the quantile regression is achieved by minimizing the quantile loss function:

[0015] In the formula, It is an asymmetric loss function; For indicator functions, when The value is 1 if the condition is met, and 0 otherwise. Take respectively and Quantile regression models the absolute distribution of prediction error directly, without assuming that the error follows any specific parameterized distribution, thus avoiding modeling bias introduced by improper assumptions about the parameter distribution.

[0016] Then, conformal prediction is used to perform calibration on an independent calibration dataset to obtain a strict coverage guarantee with a limited number of samples. On the independent calibration set... The non-consistency score is calculated for each calibration sample. This non-consistency score measures the degree to which the predicted value of that sample deviates from the actual value, and is defined as the absolute value of the prediction error.

[0017] The conformal quantiles after calibration are calculated using the coverage adjustment formula. :

[0018] In the formula, Number of samples in the calibration set; This is the set of inconsistent scores for all calibrated samples. This is a quantile function; linear interpolation is used when the quantile position is not an integer. This is a quantile position index corrected for a finite number of samples.

[0019] The core mechanism of the above coverage adjustment formula lies in: by adjusting the correction factor Multiplying by the original quantile level slightly shifts the resulting quantile value upwards, thus strictly ensuring... This holds true for any exchangeable data distribution.

[0020] For any new prediction The confidence interval for its output prediction error is:

[0021] If the error distribution exhibits significant asymmetry, then corresponding quantiles can be applied to the lower and upper bounds respectively to obtain confidence intervals with asymmetry.

[0022] Step S2: Model the spatiotemporal correlation and generate the joint confidence region.

[0023] The prediction error data is subjected to probability integral transformation to obtain the mapping value of each station error on a uniform distribution. Based on the mapping value, the spatiotemporal correlation structure of the power output prediction error among multiple new energy stations is fitted using the t-Copula function to establish a joint distribution model. Based on the joint distribution model, sampling is performed to generate a multidimensional correlation error scenario set, and a multidimensional joint confidence region covering all station errors is extracted according to the preset confidence level.

[0024] First, a probability integral transformation is performed on the error data of each station. Let... For station The empirical cumulative distribution function of prediction error is obtained by sorting historical error data and assigning empirical probability values. A probability integral transformation is then performed on each error sample for each station.

[0025] After this transformation, regardless of the original error What kind of distribution does it follow? All of them follow a uniform distribution on [0,1], thus mapping the different edge distributions of each station to the same standardized space, laying the foundation for subsequent Copula modeling.

[0026] Secondly, the robust Kendall rank correlation coefficient is used to measure the correlation between any two renewable energy power plants. and The nonlinear monotonic correlation between prediction errors is used to overcome the sensitivity of the Pearson linear correlation coefficient to outliers and heavy-tailed distributions. The measurement is based on the consistency of variable changes: for any two pairs of observations, if both change in the same direction, they are a consistent pair; if they change in opposite directions, they are an inconsistent pair. Defined as the ratio of the difference between the number of coordinated and uncoordinated pairs to the total number of pairs.

[0027] Then, Kendall Relevance parameters converted to t-Copula model The transformation relationship is as follows:

[0028] This conversion is based on Kendall The standard relationship between the correlation parameters of the elliptic Copula is thus obtained. Correlation matrix All diagonal elements are 1, and off-diagonal elements are 1. .

[0029] Next, we introduce the degree of freedom parameter. To control the degree of tail correlation, construct the t-Copula function:

[0030] In the formula, The variables for each station are uniformly distributed variables after probability integral transformation. For degrees of freedom Quantile function of a univariate t-distribution For degrees of freedom The correlation matrix is The multivariate t-distribution function.

[0031] The key technical advantage of choosing t-Copula instead of Gaussian-Copula lies in its ability to characterize the tail correlation between variables. This closely matches the physical law that multiple renewable energy power plants in the actual power grid experience significant prediction deviations simultaneously due to the same extreme weather event. Degrees of freedom The smaller the value, the stronger the tail correlation.

[0032] Finally, based on the t-Copula joint distribution model, random sampling is performed to generate a multidimensional set of related error scenarios, and the multidimensional joint confidence region is extracted. Specifically, this involves extracting from the fitted t-Copula function... Group-related uniform samples; the uniform samples are mapped back to the original error space using the empirical inverse CDF of each station, resulting in... The error vector is spatially correlated with the group space; the error vector containing exactly these samples is calculated. The minimum bounding hyperrectangular box of each sample is used as the multidimensional joint confidence region. The superrectangular mailbox is represented as follows:

[0033] The error of each station is limited to an independent interval, but the combination of these intervals takes into account the spatial correlation between stations. The hyperrectangular representation allows subsequent interval operations to be performed in closed form, avoiding tedious repeated sampling.

[0034] Step S3: Calculate the power transfer distribution factor and the reference transmission capacity.

[0035] Based on the grid parameters, the power transfer distribution factor of each new energy power station to the target grid section is calculated using the DC power flow model, and a linear sensitivity matrix between the injected power change and the power flow change of the section is established.

[0036] The power transfer distribution factor represents the change in active power flow of a transmission line or a cross-section caused by a change in the amount of active power injected at a node. Its calculation formula is as follows:

[0037] In the formula, For branch reactance matrix, This is the imaginary part of the reduced-order nodal admittance matrix.

[0038] For the target cross section Comprehensive sensitivity vector Indicates cross-section The comprehensive response of all included transmission lines to changes in the injected power of each renewable energy power station can be obtained by weighted averaging of the PTDF of each line within the cross-section. For [the section containing...] For a system with multiple coupled sections, the sensitivity vectors of each section are combined into a total sensitivity matrix. .

[0039] At the reference operating point, solve the continuous power flow problem and calculate the reference value of the cross-sectional ultimate transmission capacity that satisfies the preset safety constraints. And obtain the sensitivity coefficient of the power flow at this cross section to the change in its own transmission capacity. The mathematical description of the continuous power flow problem is as follows:

[0040] In the formula, This is the output vector of a conventional unit. For the region The power generation increment vector, This is a safety constraint vector, including line thermal stability limit constraints under N-1 anticipated faults, node voltage safety range constraints, and transient stability margin constraints. Sensitivity coefficient. Extract the corresponding elements from the Jacobian matrix at the convergence point calculated from the continuous power flow.

[0041] Step S4: Use interval calculation to determine the limit transmission capacity evaluation interval.

[0042] By combining the multidimensional joint confidence region with the linear sensitivity matrix, the evaluation interval of the cross-sectional limit transmission capability under the preset confidence level is determined through interval operations.

[0043] Near the baseline operating point, since the fluctuations in renewable energy output are usually small relative to the total system capacity, a linear approximation relationship holds between the cross-sectional power flow change and the renewable energy output deviation:

[0044] because yes A linear function, and a joint confidence region Given a hyperrectangle, the extrema of the linear function on the hyperrectangle must be found at the vertices. Furthermore, since the objective function is a linear weighted sum and the constraints on each variable are independent, the extrema can be directly obtained by combining the signs of the upper and lower bounds of each variable, without traversing all vertices. This yields the cross-section. Lower limit of the ultimate transmission capacity and upper limit Closed-form calculation formula:

[0045] In the formula, cross-section The baseline value for the ultimate transmission capacity, This represents the sensitivity coefficient of the cross-sectional power flow to changes in transmission capacity. For new energy power stations cross section The overall power transfer distribution factor, and Stations The upper and lower bounds of the prediction error. This represents the total number of new energy power stations.

[0046] The output evaluates the cross-sectional limit transmission capability under the preset signal level, including the lower limit of the limit transmission capability for each target cross-section. and upper limit The width of the transmission interval reflects the degree to which the uncertainty of new energy output affects transmission capacity. Dispatchers can directly use this interval for risk decision-making: if the current planned cross-section transmission power is lower than the lower limit of the interval, the operational risk is lower than... If the planned value is close to or exceeds the upper limit of the range, then there is a possibility of it being higher than the upper limit. Risks exceeding probability limits require preventative and control measures.

[0047] Compared with the prior art, the present invention has the following significant advantages: First, the statistical safeguards are rigorous, avoiding biases in parameter distribution assumptions. This invention employs a nonparametric method combining quantile regression and conformal prediction to construct confidence intervals for new energy output. It eliminates the need to assume that prediction errors follow a specific parameterized distribution, thus eradicating modeling biases introduced by inappropriate parameter assumptions at their source.

[0048] Second, this invention fully characterizes the spatiotemporal correlation of multiple power plants, making uncertainty assessment more realistic. This invention introduces a t-Copula function to model the joint distribution of power output prediction errors from multiple renewable energy power plants. It utilizes the Kendall rank correlation coefficient to overcome the sensitivity of Pearson linear correlation to outliers and heavy-tailed distributions. Furthermore, the tail correlation characteristics of the t-Copula accurately reflect the physical laws governing the simultaneous occurrence of significant prediction deviations from multiple power plants due to the same extreme weather event. Compared to existing studies that generally ignore or simplify the spatiotemporal correlation structure, this invention more realistically reflects the joint distribution characteristics of actual renewable energy output.

[0049] Third, computational efficiency is greatly improved, meeting the needs of online real-time applications. This invention utilizes the power transfer distribution factor to establish a linear sensitivity matrix between the power output fluctuation of new energy sources and the cross-sectional power flow change, transforming the multidimensional uncertainty propagation problem into closed-range computation, completely avoiding the computational overhead of solving the continuous power flow problem tens of thousands of times in Monte Carlo simulation.

[0050] Fourth, the assessment results directly support scheduling decisions, and risk quantification is intuitive and operable. This invention outputs upper and lower bounds of the cross-sectional transmission capacity with a clear confidence level. Schedulers can directly make risk decisions based on these ranges: if the current planned cross-sectional transmission power is lower than the lower limit of the range, the operational risk is below the significance level; if the planned value is close to the upper limit of the range, the risk of exceeding the limit can be quantified, thus achieving a transition from experience-based conservative margins to risk-aware decision-making.

[0051] Fifth, it supports joint evaluation of multiple coupled sections and has a wide range of applications. This invention extends the single-section closed-form formula to a vectorized operation of the full sensitivity matrix, which can solve the limit transmission capacity evaluation interval of all coupled sections at once. It solves the problems of high computational complexity and low efficiency of existing methods in multi-section coupled scenarios, and is suitable for online monitoring and risk assessment of the transmission capacity of sections in large regional interconnected power grids with a high proportion of new energy sources. Attached Figure Description

[0052] Figure 1 This is a flowchart of the grid limit uncertainty assessment method based on new energy power confidence in an embodiment of the present invention; Figure 2This is a schematic diagram illustrating the principle of constructing a multidimensional joint confidence region in an embodiment of the present invention; Detailed Implementation

[0053] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0054] This invention provides a method for assessing the ultimate uncertainty of the power grid based on the confidence level of new energy power, as shown in the appendix. Figure 1 As shown, this method comprises four core steps: Step 1, constructing marginal confidence intervals; Step 2, modeling spatiotemporal correlations and generating joint confidence regions; Step 3, calculating PTDF and baseline transmission capacity; and Step 4, using interval calculations to determine the ultimate transmission capacity assessment interval. These steps are sequentially linked, with the output of one step serving as the input for the next, ultimately forming a complete technical link from historical data to the transmission capacity assessment interval. The specific implementation details are described step by step below.

[0055] Step S1: Construct the marginal confidence interval.

[0056] The purpose of this step is to start from historical prediction error data and independently construct a marginal confidence interval for the power output prediction error with strict coverage statistical guarantees for each new energy power station, so as to obtain the upper and lower bounds of the prediction error for each corresponding power station.

[0057] In practice, the historical predicted power and historical actual output data of multiple renewable energy power plants in the power grid are first obtained. These renewable energy power plants include wind farms and photovoltaic power plants. For those containing... The system of the first new energy power station, recorded as the first Each venue at time The predicted power for the day is Actual output is Calculate the prediction error This creates an error dataset. This dataset is then divided into three parts: a training set, a calibration set, and a test set.

[0058] At the preset credit level Below, a typical value is 90%. A nonparametric statistical method combining quantile regression and conformal prediction is used to independently construct marginal confidence intervals for each station. The implementation of this method consists of two stages: The first stage is quantile regression. For the significance level... Define the lower quantile and upper quantile On the training set, for each station... and Solve the following quantile regression problem:

[0059] In the formula, It is an asymmetric loss function. This is an indicator function. When At that time, the penalty weight for positive residuals was only 0.05, while the penalty weight for negative residuals was as high as 0.95. The optimization process will drive... It converges to approximately the 5th quantile of the data, such that only about 5% of the sample errors are less than this value; when At that time, the weight of positive residuals was 0.95, and the weight of negative residuals was 0.05. It converges to the 95th quantile. Quantile regression does not require the assumption that the error follows any specific parameterized distribution, thus avoiding modeling bias caused by inappropriate distribution assumptions at its source.

[0060] The second stage is conformal prediction calibration. (In the independent calibration set) For each sample, a non-consistency score is calculated. This score measures the absolute degree to which the predicted value deviates from the actual value. The inconsistency scores of all calibration samples are sorted in ascending order, and the conformal quantiles after calibration are extracted using the coverage adjustment formula:

[0061] In the formula, To determine the number of samples in the calibration set, These are the corrected quantile positions for a finite sample. This correction factor is introduced to compensate for the direct selection of quantiles under finite sample conditions. The low coverage caused by quantiles means that the final interval strictly satisfies any commutative data distribution. .

[0062] For any new daily forecast The confidence interval for the power output prediction error of this station is: If the error distribution exhibits significant asymmetry, the result obtained in the first stage can be used directly. and These serve as the lower and upper bounds, respectively.

[0063] Step S2: Model the spatiotemporal correlation and generate the joint confidence region.

[0064] As attached Figure 2 As shown, the core task of this step is to perform probability integral transformation on the error data of each station obtained in step one, use the t-Copula function to fit the spatiotemporal correlation structure between multiple stations, and extract the multidimensional joint confidence region through large-scale sampling.

[0065] In practice, a probability integral transformation is first performed. Let... For the station The empirical cumulative distribution function of the prediction error is used to perform a transformation on each error sample:

[0066] After transformation, It strictly follows a uniform distribution on [0,1], thus mapping the errors of various stations with different edge distributions to the same standardized space, providing a consistent input for Copula modeling.

[0067] Then, Kendall's rank correlation coefficient was used. Measuring any two stations and Nonlinear monotonic correlation between prediction errors. Kendall The calculation is based on the consistency of variable changes: for any two pairs of observations, if they change in the same direction, they are a consistent pair; if they change in opposite directions, they are an inconsistent pair. The ratio of the difference between the number of coordinated and incoherent pairs to the total number of logs is used. Compared to Pearson's linear correlation coefficient, Kendall's... It exhibits excellent robustness to outliers and heavy-tailed distributions, making it more suitable for data with heavy-tailed characteristics, such as new energy prediction errors.

[0068] Kendall Converted to the correlation parameters in the t-Copula model, the transformation relationship is as follows: Thus, it is constructed Correlation matrix Introducing degrees of freedom parameters To control the degree of tail correlation, construct the t-Copula function:

[0069] In the formula, For degrees of freedom The quantile function of the univariate t-distribution, It is a multivariate t-distribution function. The key to choosing t-Copula instead of Gaussian-Copula is that it can characterize tail correlation—that is, the probability of multiple power stations being affected by the same extreme weather process and simultaneously experiencing large prediction deviations is significantly higher than the expected value under the normal assumption, which is highly consistent with the actual physical laws of power systems.

[0070] Finally, a large number of relevant uniform samples are extracted from the fitted t-Copula, and the original error space is mapped back using the empirical inverse CDF of each station. A set of error scenario vectors that satisfy the measured spatiotemporal correlation characteristics. For these samples, calculate the error scenario vectors that contain exactly... The minimum bounding hyperrectangular box of each sample is used as the multidimensional joint confidence region:

[0071] Each dimension of the hyperrectangle corresponds to an error interval for a station, and spatial correlation between intervals is implicitly included due to Copula sampling. The significance of using the hyperrectangle representation is that subsequent interval operations can be performed directly in closed form, without the need for repeated sampling or iterative solutions.

[0072] Step S3: Calculate PTDF and reference transmission capability.

[0073] The purpose of this step is to calculate the power transfer distribution factor of each new energy power station to each target section based on the grid parameters, establish a linear sensitivity matrix, and obtain the benchmark value of the section's ultimate transmission capacity at the benchmark operating point.

[0074] In practical implementation, the branch reactance matrix of the power grid is used. and the imaginary part of the reduced-order nodal admittance matrix Calculate the power transfer distribution factor matrix according to the DC power flow model:

[0075] The first of the matrix Each element represents a node. When the injected unit active power changes, in the line The change in active power flow caused by the above.

[0076] For the target cross section By combining the PTDF row vectors corresponding to each transmission line contained therein according to their weights, the sensitivity vector of this section to each new energy power station is obtained. If the system exists If there are several mutually coupled cross sections, then the sensitivity vectors are stacked into a full sensitivity matrix. .

[0077] At the baseline operating point, where all new energy sources output according to forecasts and conventional units are scheduled according to plan, solve the continuous power flow problem and calculate the baseline value of the cross-sectional limit transmission capacity that satisfies the N-1 safety constraint, thermal stability limit constraint, and voltage safety range constraint. Furthermore, the sensitivity coefficients of the cross-sectional power flow to changes in its transmission capacity are extracted from the Jacobian matrix of the continuous power flow convergence. .

[0078] Step S4: Use interval calculation to determine the limit transmission capacity evaluation interval.

[0079] This step will use the multidimensional joint confidence region obtained in step two. With linear sensitivity matrix By combining the baseline parameters, the evaluation interval of the cross-sectional limit transmission capacity is determined through closed-range calculation.

[0080] Near the reference operating point, the change in cross-sectional tidal current Prediction error at each station They satisfy a linear relationship The change in cross-sectional transmission capacity is Because this function is The linear weighted sum, and the joint confidence region is a hyperrectangle, means that the extreme value must be obtained at the combination of boundary values ​​of each variable. For each variable... If its coefficient If it is positive, then the greatest contribution comes from the upper bound. The minimum contribution comes from the lower bound. If the coefficient is negative, then the opposite applies. Based on this, the closed-form formula can be directly written without traversing all vertices of the hyperrectangle. The lower and upper limits of the transmission capacity of the cross section ss are respectively:

[0081] In the formula, and From the multi-dimensional joint credit region, This represents the total number of new energy power stations. The computational complexity of this closed-form formula is only... Subscalar operations, which do not involve any iterative or power flow solution processes, are the key to achieving sub-millisecond evaluation speeds.

[0082] For multi-section coupled scenarios, the above scalar operations are directly generalized to a vectorized form for the full sensitivity matrix, obtaining the evaluation intervals for all sections at once. Furthermore, when the boundary norm of the confidence region exceeds a preset threshold, the Hessian matrix is ​​numerically calculated using AC power flow perturbations, and a second-order Taylor correction is applied to ensure nonlinear accuracy under large perturbation scenarios.

[0083] Lower limit of the ultimate transmission capacity of each cross section and upper limit Output. The interval is given a confidence level. For statistical assurance, the range width directly quantifies the impact of uncertainties in renewable energy output on transmission capacity. Dispatchers use this information to make risk-aware decisions: if the planned transmission power is below the lower limit, the risk of exceeding the limit is lower. It can be executed safely; if it approaches or exceeds the limit, preventive control measures must be taken.

[0084] The following section uses the IEEE 118-node standard test system as an example to illustrate a specific application of the method of this invention.

[0085] The system comprises 118 nodes, 186 transmission lines, and 54 conventional generator units. It connects to 10 renewable energy power plants, including 6 wind farms located at nodes 10, 25, 26, 69, 80, and 87, with installed capacities of 300 MW, 250 MW, 350 MW, 400 MW, 280 MW, and 320 MW respectively; and 4 photovoltaic power plants located at nodes 54, 59, 66, and 100, with installed capacities of 200 MW, 180 MW, 240 MW, and 220 MW respectively. The total installed capacity of renewable energy is 2740 MW, representing a penetration rate of approximately 35%. Two key cross-sections were selected: Cross-section S1, the northern-central corridor, includes lines 38-65, 37-38, and 15-19, with a baseline MTC of 1320 MW; Cross-section S2, the western-eastern corridor, includes lines 65-66, 65-68, and 49-66, with a baseline MTC of 945 MW. The confidence level was set at 90%, i.e., the significance level α = 0.10. The historical data set consisted of 17,520 samples, and the test set comprised 720 operating cross-sections.

[0086] The method of this invention is executed according to steps one through four above: In step one, quantile regression and conformal prediction calibration are used to construct the marginal error interval at a 90% confidence level for each station; in step two, the degrees of freedom are... The t-Copula characterizes the spatial correlation between wind farms (correlation coefficients approximately 0.52 to 0.71), between photovoltaic power plants (correlation coefficients approximately 0.56 to 0.68), and between wind and photovoltaic power (correlation coefficients approximately 0.13 to 0.25). 50,000 correlation error scenarios are generated, and a multi-dimensional joint confidence region is extracted. In step three, the sensitivity matrix for each section is constructed, and the sensitivity coefficient of section S1 is obtained. Sensitivity coefficient of section S2 In step four, the final evaluation interval is calculated using a closed-form formula.

[0087] The calculation results are shown in Table 1.

[0088] Table 1. Evaluation results of cross-sectional ultimate transmission capacity

[0089] To verify the effectiveness and accuracy of the method of the present invention, the above calculation results were compared with the benchmark results of 50,000 Monte Carlo simulations. The comparison results are shown in Table 2.

[0090] Table 2 Comparison and verification results of the method of the present invention and Monte Carlo simulation

[0091] As shown in Tables 1 and 2, the method of this invention achieves an actual empirical coverage of 90.8% to 91.2% at a 90% nominal confidence level, strictly meeting the statistical assurance requirements; goodness of fit... The result is greater than 0.997, which is highly consistent with the Monte Carlo benchmark results. A single evaluation takes only 0.57 ms, a 357-fold speedup compared to the 203.5 ms of the Monte Carlo simulation. Furthermore, if the spatiotemporal correlation of multiple stations is ignored, i.e., assuming each station is independent, the confidence interval width will be underestimated by approximately 18% to 24%, and the empirical coverage will be only 82% to 84%, significantly lower than the nominal level of 90%, fully demonstrating the significant contribution of Copula correlation modeling to the accuracy of the evaluation.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for assessing the ultimate uncertainty of power grids based on the confidence level of new energy power, characterized in that, Includes the following steps: Step S1: Obtain historical predicted power and historical actual output data of multiple renewable energy power plants in the power grid, and construct a prediction error dataset. Based on the prediction error dataset, use a non-parametric statistical method to construct the marginal confidence interval of the output prediction error of each renewable energy power plant under a preset confidence level, and obtain the upper and lower bounds of the prediction error for each power plant. Step S2: Perform a probability integral transformation on the prediction error data to obtain the mapping value of each station's error on a uniform distribution. Based on the mapping value, use a Copula function to fit the spatiotemporal correlation structure of the output prediction errors among multiple new energy power stations and establish a joint distribution model. Based on the joint distribution model, perform sampling to generate a multidimensional correlation error scenario set, and extract a multidimensional joint confidence region covering all station errors according to the preset confidence level. Step S3: Based on the grid parameters, calculate the power transfer distribution factor of each new energy power station to the target grid section, and establish a linear sensitivity matrix between the injected power change and the power flow change of the section; Step S4: Combine the multidimensional joint confidence region with the linear sensitivity matrix, and determine the evaluation interval of the cross-sectional limit transmission capability under the preset confidence level through interval operation.

2. The method according to claim 1, characterized in that, The nonparametric statistical method is a combination of quantile regression and conformal prediction. Specifically, the quantile regression is used to fit a conditional quantile model at the quantiles corresponding to the preset confidence level to obtain an initial interval. The conformal prediction is used to calculate the inconsistency score on an independent calibration dataset, and the calibrated quantiles are calculated based on the coverage adjustment formula, thereby calibrating the initial interval to obtain a marginal confidence interval with finite sample coverage.

3. The method according to claim 2, characterized in that, The inconsistency score is the absolute value of the prediction error; the coverage adjustment formula is: in, The calibrated conformal quantiles are used to construct the inconsistency score threshold for the prediction interval; The significance level represents the allowable error rate. For the preset information level; To calibrate the number of samples in the dataset; For the first The non-consistency score of each sample; The function is a quantile function, where the first parameter is the data sequence and the second parameter is the quantile position; the marginal confidence interval is determined by adding or subtracting the calibrated quantile from the predicted power value.

4. The method according to claim 1, characterized in that, The Copula function is a t-Copula function; based on the transformed mapping value, the correlation parameter between any two renewable energy power stations is estimated using the Kendall rank correlation coefficient. To construct the correlation matrix of the t-Copula function; wherein, the correlation parameter Kendall rank correlation coefficient The conversion relationship between them is as follows: 。 5. The method according to claim 4, characterized in that, The multidimensional joint confidence region is a hyperrectangular confidence box; the method for obtaining the hyperrectangular confidence box is to extract a large number of relevant samples from the fitted Copula function, and determine the smallest circumscribed box containing the proportion of samples in the sample set at the preset confidence level, which serves as the boundary of the multidimensional joint confidence region.

6. The method according to claim 1, characterized in that, The calculation process for the evaluation interval of the cross-sectional limit transmission capacity is as follows: 1) Calculate the baseline value of the cross-sectional limit transmission capacity that satisfies the preset safety constraints at the baseline operating point, and obtain the sensitivity coefficient of the cross-sectional active power flow to the change in transmission capacity as described in the Jacobian matrix of the power flow equation. 2) Combine the upper and lower bounds of the prediction error of the multidimensional joint confidence region with the power transfer distribution factor of the corresponding power station to calculate the power fluctuation range on the target power grid section; 3) Divide the power fluctuation range by the sensitivity coefficient and sum it algebraically with the cross-sectional limit transmission capacity benchmark value to obtain the evaluation range of the cross-sectional limit transmission capacity.

7. The method according to claim 6, characterized in that, The lower and upper limits of the cross-sectional ultimate transmission capacity are calculated directly using the following closed-form formula: in, cross-section The baseline value for the ultimate transmission capacity, This represents the sensitivity coefficient of the cross-sectional power flow to changes in transmission capacity. For new energy power stations cross section The overall power transfer distribution factor, and Stations The upper and lower bounds of the prediction error. This represents the total number of new energy power stations.

8. The method according to claim 1, characterized in that, When there are multiple mutually coupled target sections in the power grid, the method further includes combining the sensitivity vectors of each section into a full sensitivity matrix, substituting the multidimensional joint confidence region into a vectorized closed-form operation, and calculating the limit transmission capacity evaluation interval of all sections in one go.

9. The method according to claim 1, characterized in that, It also includes a nonlinear correction step for the evaluation results: 1) When the boundary norm of the joint confidence region exceeds a preset threshold, calculate the Hessian matrix of the cross-sectional power flow on the output of each new energy power station; 2) Based on the second-order Taylor expansion, the interval obtained from the linear sensitivity matrix is ​​corrected by a second-order correction term, which is: ,in cross-section The trend of Heisen matrix, This is the prediction error vector.

10. The method according to claim 1, characterized in that, The new energy power stations include wind farms and photovoltaic power stations; the power transfer distribution factor is calculated based on a DC power flow model, and the formula is: in, For branch reactance matrix, This is the imaginary part of the reduced-order nodal admittance matrix.

11. The method according to claim 1, characterized in that, The preset safety constraints include the line thermal stability limit under N-1 anticipated faults, the node voltage safety range, and the transient stability margin constraint.

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