A distributed photovoltaic aggregated frequency modulation capability probability evaluation method considering distribution network operation safety constraints

Abstract

The application discloses a kind of distributed photovoltaic aggregation frequency modulation capacity probability evaluation methods considering distribution network operation safety constraint, the method first uses multivariate Gaussian mixture model to model the probability distribution of distributed photovoltaic power generation, to depict the non-Gaussian nature of multiple distributed photovoltaic output and spatial correlation;Second, with the goal of maximizing the distributed photovoltaic aggregation upward and downward power regulation range, considering distribution network line power flow constraint, node voltage safety constraint and inverter capacity constraint, a second-order cone programming model is constructed to realize the certainty evaluation of distributed photovoltaic aggregation frequency modulation capacity;Finally, a multivariate mixed Gaussian point estimation algorithm is proposed, which constructs a special sampling set and performs a small amount of deterministic calculation, and obtains the probability distribution of distributed photovoltaic aggregation frequency modulation reserve capacity by combining statistical analysis and weighted mixing.The method effectively analyzes the large-scale distributed photovoltaic aggregation frequency modulation capacity and quantifies its uncertainty, and considers the calculation accuracy and efficiency.

Description

Technical Field

[0001] This invention relates to a probabilistic assessment method for the frequency regulation capability of distributed photovoltaic aggregation considering the safety constraints of distribution network operation, belonging to the field of power system uncertainty analysis. Background Technology

[0002] With the large-scale integration of distributed photovoltaic (PV) power, the overall inertia of the power system is rapidly shrinking, and its frequency regulation capability is continuously declining. The large number of distributed PV units integrated into the distribution network has the potential to actively participate in power system frequency regulation. Fully exploring and utilizing the aggregated frequency support capability of distributed PV in the distribution network is of great significance for improving the operational safety of new energy power systems. However, distributed PV differs from traditional synchronous generators; its power generation and available frequency regulation capability are highly random, influenced by external factors such as solar irradiance, ambient temperature, and system operating status. Therefore, distributed PV faces significant uncertainty challenges when providing frequency support services to the grid.

[0003] Furthermore, large-scale distributed photovoltaic (PV) grid integration leads to safety risks in the distribution network, such as power backflow and node voltage exceeding limits. According to relevant grid connection standards, distributed PV requires adjusting the reactive power output of inverters to participate in distribution network voltage regulation. Therefore, while supporting system frequency, distributed PV must also consider the local operational safety of the distribution network. Because transmission system operators cannot directly perceive the aggregation and frequency regulation capabilities of massive, dispersed distributed PV systems, and existing deterministic assessment methods cannot handle the randomness of PV output, the potential for distributed PV aggregation and frequency regulation is insufficiently explored. Existing probabilistic assessment methods, such as Monte Carlo simulations, involve enormous computational demands and are insufficient for online assessment requirements; while traditional point estimation methods typically assume that the input random variables follow a Gaussian distribution, failing to handle the non-Gaussian nature and complex spatiotemporal correlations of distributed PV output, leading to inaccurate probabilistic assessment results. Therefore, an accurate and efficient assessment method is urgently needed to fully consider the uncertainty of distributed PV power generation and the safety requirements of the distribution system, and to explore and assess the large-scale distributed PV aggregation and frequency regulation capabilities. Summary of the Invention

[0004] To address the limitations of related background technologies, this invention provides a probabilistic assessment method for the frequency regulation capability of distributed photovoltaic (PV) power aggregation considering distribution network operation safety constraints. First, a multivariate Gaussian mixture model is used to describe the probability distribution of distributed PV power generation, accurately characterizing the non-Gaussian nature and multivariate correlation of distributed PV power generation. Second, a distributed PV frequency regulation capability assessment model considering network-level power flow, voltage safety constraints, and equipment-level inverter capacity constraints is constructed to uncover the large-scale distributed PV frequency regulation capability. Finally, by integrating the Gaussian mixture model with a point estimation algorithm, the probability distribution of the distributed PV frequency regulation capability is obtained through a small amount of deterministic calculation and statistical analysis.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A probabilistic assessment method for the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints includes the following steps:

[0007] 1) A multivariate Gaussian mixture model is used to model and characterize the joint probability distribution of multiple distributed photovoltaic power generation in the distribution network to obtain the joint probability density function;

[0008] 2) Construct an objective function to maximize the upward and downward power regulation of distributed photovoltaic aggregation, and use the power flow constraints of the distribution network, the safe operation constraints of the distribution network, and the capacity constraints of the distributed photovoltaic inverter as constraints. Combine this with second-order cone programming to construct a distributed photovoltaic aggregation frequency regulation capability evaluation model.

[0009] 3) Combining the basic principles of decorrelation transformation and point estimation methods, several distributed photovoltaic power generation sample points corresponding to each Gaussian component in the multivariate Gaussian mixture model are generated, and then a distributed photovoltaic power generation sample set is constructed.

[0010] 4) Substitute each generated sample into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain a sample set of distributed photovoltaic aggregation frequency regulation capability;

[0011] 5) Based on the sample set of distributed photovoltaic aggregation frequency regulation capability, statistical moments of the distributed photovoltaic aggregation frequency regulation capability sample are calculated, and weighted mixing is performed according to the weight of each Gaussian component to obtain the probability distribution of distributed photovoltaic aggregation frequency regulation capability in Gaussian mixture form.

[0012] Furthermore, in step 1), the joint probability density function is obtained by weighted superposition of multiple Gaussian components; each Gaussian component has a corresponding weight coefficient, the sum of all weight coefficients is 1 and all are non-negative, each Gaussian component is described by a mean vector and a covariance matrix, and the whole is used to accurately fit the joint probability distribution of the output power of multiple distributed photovoltaics, fully reflecting its non-Gaussian and spatial correlation.

[0013] Furthermore, in step 2), the core of the objective function is to maximize the sum of the aggregated upward power regulation, the aggregated downward power regulation, and the active power loss of all branches of the distribution network; wherein, the aggregated upward power regulation is obtained based on the aggregated upward power regulation of each distributed photovoltaic power generation and the corresponding linearization constant, and the aggregated downward power regulation is obtained based on the aggregated downward power regulation of the distributed photovoltaic power generation and the corresponding linearization constant.

[0014] Furthermore, in step 2), the constraints specifically include:

[0015] The power flow constraints of the distribution network are described by using the DistFlow model after second-order cone relaxation, which clarifies the relationship between branch active power, reactive power and node voltage and current.

[0016] The safety constraints for distribution network operation are: the square of the branch current amplitude shall not exceed the square of the maximum current allowed to flow through the branch, and the square of the node voltage amplitude shall be maintained between the square of the set safe upper limit and the square of the safe lower limit of the node voltage.

[0017] The capacity constraints for distributed photovoltaic (PV) inverters are as follows: the active power output of distributed PV is equal to its maximum available active power minus the upward power regulation, and the active power output of distributed PV is not less than the downward power regulation; the combination of active and reactive power must meet the inverter's nominal capacity limit; the value of the upward power regulation ranges from 0 to the product of the maximum allowable upward reserve ratio and the inverter's nominal capacity, and the value of the downward power regulation ranges from 0 to the product of the maximum allowable downward reserve ratio and the inverter's nominal capacity.

[0018] Further, in step 3), the distributed photovoltaic power generation sample set is obtained through the following steps: For each Gaussian component in the multivariate Gaussian mixture model, the original correlated distributed photovoltaic power generation vectors are first processed using the Cholesky decomposition technique to obtain mutually independent distributed photovoltaic power generation vectors; then, combined with the two-point estimation method, sampling is performed in the transformed mutually independent distributed photovoltaic power generation vector space, with sampling points divided into two cases: down-skewed and up-skewed. The specific sampling values ​​are determined based on the mean, standard deviation, third-order central moment, and number of distributed photovoltaics of the corresponding Gaussian components; finally, the independent sampling points are restored to the original space through inverse transformation to form a distributed photovoltaic power generation sample that takes into account correlation, thereby constructing a distributed photovoltaic power generation sample set.

[0019] Furthermore, in step 4), each generated sample is substituted into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain the distributed photovoltaic aggregation frequency regulation capability sample set. The specific process is as follows:

[0020] Each power sample vector in the sample set is regarded as a deterministic scenario of the maximum available power of distributed photovoltaic at a certain moment. They are then substituted into the evaluation model constructed in step 2) one by one. By solving the model, the sample values ​​of the aggregated upward frequency regulation capability and the aggregated downward frequency regulation capability of distributed photovoltaic are obtained for each scenario. The sample values ​​of all scenarios together constitute the sample set of the aggregated frequency regulation capability of distributed photovoltaic, providing data support for subsequent probability assessment.

[0021] Further, in step 5), the step of calculating the statistical moments of the distributed photovoltaic (PV) aggregated frequency modulation (EPM) capability samples based on the distributed PV aggregated frequency modulation capability sample set, and then performing a weighted mixture based on the weights of each Gaussian component to obtain a Gaussian mixture form of the distributed PV aggregated frequency modulation capability probability distribution, specifically includes:

[0022] First, based on the sample values ​​of aggregated upward and downward frequency modulation capabilities obtained in step 4), and combined with the weight coefficients corresponding to the samples, the mean and standard deviation of aggregated upward and downward frequency modulation capabilities under each Gaussian component are calculated respectively. Then, according to the weight of each Gaussian component, the mean and standard deviation corresponding to all Gaussian components are weighted and mixed to finally construct the probability distribution of aggregated upward and downward frequency modulation capabilities of distributed photovoltaic power in Gaussian mixture form.

[0023] A computer-readable storage medium having computer instructions stored thereon for causing a computer to perform the steps of any of the methods described.

[0024] An electronic device, comprising:

[0025] One or more processors;

[0026] Memory, used to store one or more programs;

[0027] When the one or more programs are executed by the one or more processors, the one or more processors perform any of the methods described.

[0028] The beneficial effects of this invention are as follows:

[0029] By introducing a multivariate Gaussian mixture model to model distributed photovoltaic (PV) power generation, this approach effectively overcomes the limitations of traditional probabilistic assessment methods that typically assume input variables follow a normal distribution or are mutually independent. It accurately characterizes the inherent non-Gaussianity, multi-peak characteristics, and complex spatiotemporal correlations caused by geographical proximity in large-scale distributed PV output, thus ensuring the accuracy of the description of uncertain input information. Furthermore, by constructing a distributed PV aggregation frequency regulation capability assessment model based on second-order cone programming, it can strictly guarantee the voltage safety of the distribution network and inverter capacity limitations, while fully exploring the distributed PV aggregation frequency regulation capability. The proposed mixture point estimation algorithm transforms the complex probabilistic assessment problem into a finite number of deterministic calculations, significantly improving computational efficiency compared to Monte Carlo simulation. This meets the needs of online assessment and provides technical support for grid dispatching departments to grasp the system's regulation potential and formulate safe and reliable dispatching plans. Attached Figure Description

[0030] Figure 1 This is a probability assessment process for distributed photovoltaic aggregation frequency regulation capability according to an embodiment of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention provide a probabilistic assessment method for distributed photovoltaic aggregation frequency regulation capability considering distribution network operation safety constraints, the process of which is as follows: Figure 1 As shown.

[0032] Example:

[0033] A probabilistic assessment method for the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints includes the following steps:

[0034] 1) A multivariate Gaussian mixture model is used to model and characterize the joint probability distribution of multiple distributed photovoltaic power generation in the distribution network to obtain the joint probability density function;

[0035] 2) Construct an objective function to maximize the upward and downward power regulation of distributed photovoltaic aggregation, and use distribution network power flow constraints, network operation safety constraints, and distributed photovoltaic inverter capacity constraints as constraints. Combine second-order cone programming to construct a distributed photovoltaic aggregation frequency regulation capability evaluation model.

[0036] 3) Combining the basic principles of decorrelation transformation and point estimation methods, several distributed photovoltaic power generation sample points corresponding to each Gaussian component in the multivariate Gaussian mixture model are generated, and then a distributed photovoltaic power generation sample set is constructed.

[0037] 4) Substitute each generated sample into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain a sample set of distributed photovoltaic aggregation frequency regulation capability;

[0038] 5) Based on the sample set of distributed photovoltaic aggregation frequency regulation capability, statistical moments of the distributed photovoltaic aggregation frequency regulation capability sample are calculated, and weighted mixing is performed according to the weight of each Gaussian component to obtain the probability distribution of distributed photovoltaic aggregation frequency regulation capability in Gaussian mixture form.

[0039] (1) First, the joint probability density function is obtained by modeling and characterizing the joint probability distribution of multiple distributed photovoltaic power generation in the distribution network using a multivariate Gaussian mixture model.

[0040] Given that the output power of distributed photovoltaic (PV) systems is affected by meteorological factors such as cloud cover and temperature variations, its probability distribution exhibits significant non-Gaussian characteristics (e.g., skewed or multimodal distribution). Furthermore, there is strong spatiotemporal correlation between geographically proximate distributed PV power plants. To accurately describe this complex joint probability distribution, this invention employs a weighted sum of a finite number of multivariate Gaussian distributions to approximate the true joint probability density function.

[0041] Assuming there is in the distribution network A vector composed of the random variables of the power output of a distributed photovoltaic system is denoted as . The joint probability density function of distributed photovoltaic power generation Specifically, it is expressed as follows:

[0042] ;

[0043] Among them, the probability density function of multivariate Gaussian components Expanded to:

[0044] ;

[0045] In the formula: for A vector consisting of random variables representing the output power of distributed photovoltaic systems; The output power of potentially achievable distributed photovoltaic power; The number of Gaussian components in the Gaussian mixture model; For the first The weight coefficients corresponding to each Gaussian component represent the proportion of that component in the mixture model, and satisfy the following conditions: ; For the first The mean vector of each Gaussian component reflects the center position of that component; For the first The covariance matrix of the Gaussian components reflects the correlation and dispersion among variables. This model can decompose complex probability distributions of arbitrary shapes into several easily tractable Gaussian distributions, laying a mathematical foundation for subsequent probabilistic assessment of distributed photovoltaic aggregation frequency regulation capabilities based on Gaussian mixture point estimation.

[0046] (2) Construct a distributed photovoltaic aggregation frequency regulation capability evaluation model. The model aims to maximize the upward and downward power regulation of distributed photovoltaic aggregation, and takes into account constraints such as power flow of distribution network lines, node voltage security and apparent power capacity of distributed photovoltaic inverters. It also uses the second-order cone relaxation technique to handle nonlinear constraints.

[0047] First, the objective function for evaluation is determined. The core of evaluating the frequency regulation capability of distributed photovoltaic (PV) aggregation lies in quantifying the maximum upward and downward power regulation potential that the distribution network as a whole can provide to the upstream grid. Therefore, the objective function is set to maximize the upward power regulation of distributed PV aggregation. and the amount of downward power adjustment of the polymer The sum. Furthermore, to ensure the tightness of the second-order cone relaxation in the subsequent radial distribution network power flow model, a distribution network active power line loss term is introduced into the objective function, thus constructing the objective function of the distributed photovoltaic aggregation frequency regulation capability evaluation model as follows:

[0048] ;

[0049] ;

[0050] In the formula: and These represent the maximum aggregated upward and aggregated downward power regulation provided for distributed photovoltaic power, respectively. It is the set of all branches of the distribution network; Indicates the connection node and nodes The side road; branch road The resistance; For flow through branch road The square of the current amplitude; This refers to the number of distributed photovoltaic power generation systems in the power distribution network. and The first The maximum up and down power regulation provided by a single distributed photovoltaic system; For the first The linearization constants corresponding to each distributed photovoltaic (PV) system are used to describe the relationship between the active power injection of distributed PV systems and the power output of substations.

[0051] Establish a power flow model and operational safety constraints for a distribution network. Traditional nonlinear power flow equations are nonconvex, making it difficult to guarantee a globally optimal solution. This invention uses the second-order cone relaxation form of the DistFlow branch power flow model to describe the relationship between node voltages and injected power in the distribution network. The complete power flow equations for the distribution network are expressed as follows:

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] The constraints for safe operation of the power distribution network are expressed as follows:

[0057] ;

[0058] ;

[0059] In the formula: and They are respectively the branches through which the flow passes Active power and reactive power; This indicates that the node is a downstream node of the node; and The first The active and reactive power output of a distributed photovoltaic system; and Representing nodes respectively Active and reactive loads at the location; branch road The reactance; For nodes The square of the voltage amplitude; Represents the L2 norm; branch road The maximum current that is allowed to flow; and These are the upper and lower limits for safe node voltage, respectively.

[0060] Finally, capacity constraints for distributed photovoltaic (PV) inverters are established. To provide frequency support, distributed PV needs to reserve a certain amount of active power, and its output power is limited by the inverter's apparent power capacity. These distributed PV inverter capacity constraints are specifically expressed as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] In the formula: and The first The active and reactive power output of a distributed photovoltaic system. For the first The maximum available active power of a distributed photovoltaic system is a random variable. For the first The nominal capacity of a distributed photovoltaic inverter; and These are the maximum permissible upward and downward reserve ratio coefficients, respectively.

[0067] (3) Combining the basic principles of decorrelation transformation and point estimation, several distributed photovoltaic power generation sample points corresponding to each Gaussian component in the multivariate Gaussian mixture model are generated, and then a distributed photovoltaic power generation sample set is constructed. For each Gaussian component in the multivariate Gaussian mixture model, a sample set is constructed by combining the basic principle of the two-point estimation method, and the correlation between distributed photovoltaic power output is processed by Cholesky decomposition technology.

[0068] Specifically, regarding the first multivariate Gaussian mixture model... Gaussian components Combining the basic principles of the two-point estimation method, a finite number of sample points are drawn from the joint probability distribution of continuous distributed photovoltaic power generation. If there are... For a distributed photovoltaic system, it is necessary to construct... Sample points. Considering the spatial correlation among distributed photovoltaic power outputs, the covariance matrix of each Gaussian component. Since it is a non-diagonal matrix, direct sampling will lose correlation information. This is specifically addressed for the first element in a multivariate Gaussian mixture model. Each component is used to handle correlations using the Cholesky decomposition technique:

[0069] ;

[0070] ;

[0071] In the formula: In the multivariate Gaussian mixture model, the first... The covariance matrix corresponding to each Gaussian component; This is the lower triangular matrix obtained through Cholesky decomposition; This represents the original related distributed photovoltaic power vector; These are the transformed, independent distributed photovoltaic power vectors;

[0072] Then, combining the principle of the two-point estimation method, sampling is performed in the transformed, mutually independent distributed photovoltaic power vector space, with sampling points... Configured as follows:

[0073] ;

[0074] In the formula: and They represent the transformed th The first Gaussian component Mean and standard deviation of distributed photovoltaic power generation; Indicates downward deviation. Indicates upward deviation; The position coefficient is specifically defined as:

[0075] ;

[0076] ;

[0077] In the formula: For the transformed corresponding to the first The first Gaussian component The third-order central moment of a distributed photovoltaic power generation capacity;

[0078] After obtaining independent distributed photovoltaic power generation samples, inverse transformation is then performed. Transform it back to the original space to obtain a sample of distributed photovoltaic power generation that takes correlation into account. Further construct a sample set of distributed photovoltaic power generation. :

[0079] ;

[0080] In the formula: For the corresponding to the first The first Gaussian component The power sampling vector corresponding to the nth distributed photovoltaic system, the th The sampling points corresponding to each distributed photovoltaic power generation are: The sampled values ​​of the remaining distributed photovoltaic systems are set as the mean, i.e.:

[0081] ;

[0082] In the formula: Indicates the first In the probability distribution of distributed photovoltaic power generation, the first... The mean of the Gaussian components.

[0083] (4) Substitute each generated sample into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain the distributed photovoltaic aggregation frequency regulation capability sample set. The distributed photovoltaic power generation sample set generated in step 3) is then used for this purpose. Each sample vector in the model is considered a deterministic scenario of the maximum available power of distributed photovoltaic power at a certain moment. For the first sample vector in the multivariate Gaussian mixture model... Each component contains a total of [number] components. Such a scenario.

[0084] Secondly, each sample vector Substitute the specific numerical values ​​into the distributed photovoltaic aggregation frequency regulation capability evaluation model constructed in step 2) to obtain... A deterministic second-order cone programming subproblem. Using a solver to solve this... The second-order cone programming subproblems are solved sequentially. This step transforms the original nonlinear programming problem containing random variables into a second-order cone programming (SOCP) problem of finite degree.

[0085] Finally, samples of the distributed photovoltaic aggregation upmodulation capability obtained from solving each sub-problem are extracted. Sample of distributed photovoltaic aggregation down-modulation capability This process can be mathematically abstracted as a nonlinear mapping:

[0086] ;

[0087] In the formula: This is a vector composed of sample values ​​of the frequency regulation capability of distributed photovoltaic power generation. This represents a complex nonlinear distributed photovoltaic aggregation frequency regulation capability evaluation model that includes power flow equations, security constraints, and inverter constraints.

[0088] (5) Based on the sample set of distributed photovoltaic aggregation frequency regulation capabilities, the statistical moments of the distributed photovoltaic aggregation frequency regulation capability samples are statistically analyzed, and a weighted mixture is performed according to the weight of each Gaussian component to obtain the probability distribution of distributed photovoltaic aggregation frequency regulation capability in Gaussian mixture form. The specific process is as follows:

[0089] Calculate the upward and downward power regulation of distributed photovoltaic aggregation with respect to the first... Mean and standard deviation of each Gaussian component:

[0090] ;

[0091] ;

[0092] In the formula: and The upward frequency modulation capability of distributed photovoltaic aggregation corresponds to the first The mean and standard deviation of each Gaussian component; and The upward frequency modulation capability of distributed photovoltaic aggregation corresponds to the first The mean and standard deviation of each Gaussian component; The weight coefficients corresponding to the output samples are calculated as follows:

[0093] , .

[0094] Finally, based on the idea of ​​the law of total probability, it is assumed that the output distribution of a nonlinear system also follows a Gaussian mixture distribution. This is achieved by utilizing the weights of all Gaussian components. The corresponding output mean and standard deviation are used to reconstruct the probability distribution function of the upward frequency modulation capability of distributed photovoltaic aggregation in Gaussian mixture form. and the probability distribution function of down-modulation capability of distributed photovoltaic aggregation :

[0095] ;

[0096] This analytical expression fully describes the probabilistic characteristics of distributed photovoltaic aggregation frequency regulation capability under the consideration of uncertainties and grid security constraints.

[0097] Furthermore, to verify the effectiveness of the distributed photovoltaic (PV) aggregation frequency regulation capability probabilistic assessment method proposed in this invention, simulation analysis was performed on improved IEEE 33-node and IEEE 123-node distribution systems. To quantify the error level of various distributed PV aggregation frequency regulation capacity uncertainty analysis methods, a quantile level deviation index was introduced. This index divides the quantile level within the range of [5%, 95%] into 19 nominal quantile levels, with an interval of 5% between adjacent nominal quantile levels. The quantiles corresponding to the output random variables were calculated, and a large sample size (sampling number set to 5 × 10⁻⁶) was used. 4 Using Monte Carlo simulation (MCS) results as a benchmark, the approximate error of quantiles calculated by different methods at each nominal quantile level is statistically analyzed. The specific definition of this indicator is as follows:

[0098] ;

[0099] In the formula: Indicates the first The nth output random variable (i.e., the distributed photovoltaic aggregated frequency regulation capacity) is the nth... Quantile level deviation; This indicates the number of samples generated by the Monte Carlo simulation; This is an indicator function that takes the value 1 when the condition is met and 0 otherwise. The Monte Carlo simulation generated the first The first output random variable Each sample value; Indicates the first value calculated by the method to be evaluated. The output random variable at the nominal quantile level The quantile below. This indicator can intuitively reflect the difference between the uncertainty analysis results and the true probability distribution.

[0100] Table 1. Comparison of accuracy between the proposed method and the traditional two-point estimation method under different system scales (unit: %)

[0101] Table 1 presents a comparison of the evaluation accuracy of the proposed method and the traditional two-point estimation method on IEEE 33-node and IEEE 123-node systems. The statistical data in Table 1 shows that the traditional two-point estimation method has a large computational error on the IEEE 33-node test system, with an average quantile deviation of approximately 6% and a maximum quantile deviation as high as 18.6080%. This is mainly because the traditional method assumes that the random variables follow a single Gaussian distribution, which cannot adapt to the skewed and multi-peak characteristics of distributed photovoltaic power output. In contrast, the point estimation algorithm based on a multivariate Gaussian mixture model proposed in this invention reduces the average quantile deviation on the IEEE 33-node system to 0.1836%, with a maximum deviation of only 0.7160%, achieving nearly 30 times the accuracy improvement compared to the traditional method. On the larger-scale IEEE 123-node test system, the advantages of the proposed method remain significant, with the corresponding average quantile deviation stabilizing at around 0.15% and the maximum quantile deviation not exceeding 0.30%, improving the accuracy of uncertainty analysis by nearly 40 times compared to the traditional two-point estimation method. The above comparative analysis verifies the effectiveness of the method of the present invention on different test systems, and its accuracy in the probability assessment of distributed photovoltaic aggregation frequency regulation capacity far exceeds that of the traditional two-point estimation method.

[0102] Table 2 Comparison of computation time for different methods under different system scales (unit: seconds)

[0103] Table 2 presents a comparison of the computation time of the method of this invention, Monte Carlo simulation (MCS), and the traditional two-point estimation method under different system sizes. As can be seen from Table 2, the Monte Carlo simulation method requires tens of thousands of deterministic capacity assessment calculations to obtain convergent probability distribution results, leading to a sharp increase in computation time with system size. On the IEEE 33-node system, MCS takes 1.81 × 10⁻⁶ hours. 4 Seconds; and on the IEEE 123-node system, due to the dramatic increase in the dimensionality of variables and the problem size, the computation time climbs even higher to 4.74 × 10⁻⁶ seconds. 4 The current speed of calculation is clearly insufficient for online real-time evaluation. While the traditional two-point estimation method offers the fastest computation speed, as mentioned earlier, its accuracy is insufficient for engineering requirements. The method of this invention only requires execution... A single deterministic calculation is sufficient to achieve a high-precision assessment of the probability distribution of distributed photovoltaic (PV) aggregated frequency modulation (EPCM) capacity. On an IEEE 33-bus system, the method of this invention requires only 10.78 seconds; on an IEEE 123-bus system, the computation time is 38.96 seconds. Although the computation time is slightly longer than the traditional point estimation method (due to the need to calculate multiple Gaussian components), the computational efficiency is improved by approximately three orders of magnitude (approximately 1200 times faster) compared to Monte Carlo simulation. The simulation results at different system scales demonstrate that the method of this invention has high computational efficiency and is applicable to the uncertainty analysis of distributed PV aggregated frequency modulation capacity across various system scales.

[0104] The specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, which are not intended to limit the scope of protection of the present invention. All equivalent models or equivalent algorithm flows made using the content of the present invention specification and drawings, and which are directly or indirectly applied to other related technical fields, are within the scope of patent protection of the present invention.

Claims

1. A probabilistic assessment method for the aggregated frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints, characterized in that, Includes the following steps: 1) A multivariate Gaussian mixture model is used to model and characterize the joint probability distribution of multiple distributed photovoltaic power generation in the distribution network to obtain the joint probability density function; 2) Construct an objective function to maximize the upward and downward power regulation of distributed photovoltaic aggregation, and use the power flow constraints of the distribution network, the safe operation constraints of the distribution network, and the capacity constraints of the distributed photovoltaic inverter as constraints. Combine this with second-order cone programming to construct a distributed photovoltaic aggregation frequency regulation capability evaluation model. 3) Combining Cholesky decomposition technique and two-point estimation method, several distributed photovoltaic power generation sample points corresponding to each Gaussian component in the multivariate Gaussian mixture model are generated, and then a distributed photovoltaic power generation sample set is constructed. 4) Substitute each generated sample into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain a sample set of distributed photovoltaic aggregation frequency regulation capability; 5) Based on the sample set of distributed photovoltaic aggregation frequency regulation capability, statistical moments of the distributed photovoltaic aggregation frequency regulation capability sample are calculated, and weighted mixing is performed according to the weight of each Gaussian component to obtain the probability distribution of distributed photovoltaic aggregation frequency regulation capability in Gaussian mixture form.

2. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 1, characterized in that, In step 1), the joint probability density function is obtained by weighted superposition of multiple Gaussian components; each Gaussian component has a corresponding weight coefficient, the sum of all weight coefficients is 1 and all are non-negative, each Gaussian component is described by a mean vector and a covariance matrix, and the whole is used to accurately fit the joint probability distribution of the output power of multiple distributed photovoltaics, fully reflecting its non-Gaussian and spatial correlation.

3. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 1, characterized in that, In step 2), the core of the objective function is to maximize the sum of the aggregated upward power regulation, the aggregated downward power regulation, and the active power loss of all branches of the distribution network. The aggregated upward power regulation is obtained based on the aggregated upward power regulation of each distributed photovoltaic power generation unit and the corresponding linearization constant, and the aggregated downward power regulation is obtained based on the aggregated downward power regulation of the distributed photovoltaic power generation unit and the corresponding linearization constant.

4. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 3, characterized in that, In step 2), the constraints specifically include: The power flow constraints of the distribution network are described by using the DistFlow model after second-order cone relaxation, which clarifies the relationship between branch active power, reactive power and node voltage and current. The safety constraints for distribution network operation are: the square of the branch current amplitude shall not exceed the square of the maximum current allowed to flow through the branch, and the square of the node voltage amplitude shall be maintained between the square of the set safe upper limit and the square of the safe lower limit of the node voltage. The capacity constraints for distributed photovoltaic (PV) inverters are as follows: the active power output of distributed PV is equal to its maximum available active power minus the upward power regulation, and the active power output of distributed PV is not less than the downward power regulation; the combination of active and reactive power must meet the inverter's nominal capacity limit; the value of the upward power regulation ranges from 0 to the product of the maximum allowable upward reserve ratio and the inverter's nominal capacity, and the value of the downward power regulation ranges from 0 to the product of the maximum allowable downward reserve ratio and the inverter's nominal capacity.

5. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 1, characterized in that, In step 3), the distributed photovoltaic power generation sample set is obtained through the following steps: For each Gaussian component in the multivariate Gaussian mixture model, the original correlated distributed photovoltaic power generation vectors are first processed using the Cholesky decomposition technique to obtain mutually independent distributed photovoltaic power generation vectors; then, combined with the two-point estimation method, sampling is performed in the transformed mutually independent distributed photovoltaic power generation vector space, with sampling points divided into two cases: down-skewed and up-skewed. The specific sampling values ​​are determined based on the mean, standard deviation, third central moment, and number of distributed photovoltaics of the corresponding Gaussian components; finally, the independent sampling points are restored to the original space through inverse transformation to form a distributed photovoltaic power generation sample that takes into account correlation, thereby constructing a distributed photovoltaic power generation sample set.

6. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 5, characterized in that, In step 4), each generated sample is substituted into the distributed photovoltaic aggregation frequency regulation capability assessment model for deterministic calculation to obtain the sample set of distributed photovoltaic aggregation frequency regulation capability. The specific process is as follows: Each power sample vector in the sample set is regarded as a deterministic scenario of the maximum available power of distributed photovoltaic at a certain moment. They are then substituted into the evaluation model constructed in step 2) one by one. By solving the model, the sample values ​​of the aggregated upward frequency regulation capability and the aggregated downward frequency regulation capability of distributed photovoltaic are obtained for each scenario. The sample values ​​of all scenarios together constitute the sample set of the aggregated frequency regulation capability of distributed photovoltaic, providing data support for subsequent probability assessment.

7. The method for probabilistically evaluating the frequency regulation capability of distributed photovoltaic power generation considering distribution network operation safety constraints as described in claim 6, characterized in that, In step 5), the statistical moments of the distributed photovoltaic (PV) aggregated frequency modulation (EPM) capability samples are calculated based on the sample set of distributed PV aggregated frequency modulation capabilities, and a weighted mixture is performed according to the weights of each Gaussian component to obtain a Gaussian mixture form of the probability distribution of distributed PV aggregated frequency modulation capabilities. Specifically, this includes: First, based on the sample values ​​of aggregated upward and downward frequency modulation capabilities obtained in step 4), and combined with the weight coefficients corresponding to the samples, the mean and standard deviation of aggregated upward and downward frequency modulation capabilities under each Gaussian component are calculated respectively. Then, according to the weight of each Gaussian component, the mean and standard deviation corresponding to all Gaussian components are weighted and mixed to finally construct the probability distribution of aggregated upward and downward frequency modulation capabilities of distributed photovoltaic power in Gaussian mixture form.

8. A computer-readable storage medium storing computer instructions thereon, characterized in that, The computer instructions are used to cause the computer to perform the steps of the method as described in any one of claims 1-7.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-7.

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