Power system frequency stability probability assessment method, system, device and medium

Abstract

This invention relates to the field of power system technology, and more particularly to a method, system, device, and medium for probabilistic assessment of power system frequency stability. This method probabilistically models the power deficit and probability of occurrence corresponding to anticipated faults, and establishes correlated wind and solar power output scenarios by combining historical wind speed and solar irradiance. Power deficit, wind power output, and solar power output are unified as three-dimensional input parameters. A three-dimensional polynomial chaotic expansion surrogate model is constructed using transient time-domain simulation results with finite collocation points, thereby enabling rapid determination of frequency stability indicators under various joint scenarios. Simultaneously, by jointly weighting the frequency stability indicator exceedance results with the corresponding fault occurrence probability and wind and solar scenario probability, the frequency exceedance risk can be obtained, simultaneously reflecting the differences in fault types and the impact of new energy output fluctuations, thus improving the accuracy of frequency stability assessment.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method, system, device and medium for probabilistic assessment of power system frequency stability. Background Technology

[0002] Frequency is one of the core indicators for measuring the power quality and operational safety of a power system. In traditional power systems, frequency stability analysis is usually based on time-domain simulation evaluation of a set of anticipated severe fault scenarios to verify the system's ability to maintain frequency under high-power disturbances.

[0003] However, new energy generating units are connected to the grid via power electronic converters, and their physical characteristics differ fundamentally from those of traditional synchronous generators. Specifically, they lack rotational inertia and do not actively participate in primary frequency regulation. Furthermore, with the significant decrease in the equivalent inertia of the power system, the frequency stability problem after experiencing high-power disturbances (such as large unit tripping or DC blocking) is becoming increasingly prominent.

[0004] Against this backdrop, the uncertainty of power systems is evolving from a single dimension to a multi-dimensional superposition. On the one hand, the randomness and volatility of new energy output cause the system operating point to change continuously, resulting in uncertainty in the system state before a fault. On the other hand, the types of faults the system may encounter are also uncertain; that is, different faults correspond to different power deficits, and their impact on frequency varies greatly. The superposition of these two uncertainties poses a challenge to traditional deterministic frequency stability analysis methods.

[0005] Currently, existing technologies are inefficient at assessing the frequency stability of power systems and cannot fully cover uncertain probabilistic risks, resulting in poor accuracy in assessing the frequency stability of power systems. Summary of the Invention

[0006] In view of this, in order to solve the above-mentioned technical problems, the present invention provides a method, system, device and medium for probabilistic assessment of frequency stability in power systems.

[0007] The first aspect of this invention provides a method for probabilistic assessment of frequency stability in a power system, the method comprising: Based on the anticipated fault set of the target power system, determine the power deficit and occurrence probability corresponding to each anticipated fault, and establish the power deficit probability distribution. Based on the historical wind speed data and historical solar intensity data of the target power system, a joint probability distribution of wind and solar power output is established, and multiple wind and solar power output scenarios are generated. Using the power deficit, wind power output, and photovoltaic power output as three-dimensional input parameters, multiple collocation points are selected in the three-dimensional parameter space corresponding to the three-dimensional input parameters. Transient time-domain simulation is performed on the system operation scenario corresponding to each collocation point to obtain the frequency stability index corresponding to each collocation point. A three-dimensional polynomial chaotic expansion surrogate model is constructed based on each collocation point and its corresponding frequency stability index. Multiple power deficit samples are obtained based on the power deficit probability distribution. Each power deficit sample is combined with the multiple wind and solar power output scenarios to obtain multiple joint scenarios. The frequency stability index corresponding to each joint scenario is determined using the three-dimensional polynomial chaotic expansion surrogate model. Based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, the over-limit result of each joint scenario is determined. Then, based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario, the over-limit result is weighted by joint probability to obtain the frequency over-limit risk of the target power system.

[0008] In one example, the determination of the power deficit and its probability of occurrence corresponding to each anticipated fault based on the anticipated fault set of the target power system, and the establishment of a power deficit probability distribution, includes: Based on the safety verification requirements of the target power system, a set of anticipated faults, including multiple anticipated faults, is determined; Based on the actual operating power of the transmission channel corresponding to each of the anticipated faults before its occurrence, determine the power deficit corresponding to each of the anticipated faults. Based on the historical fault statistics of each of the aforementioned anticipated faults, the probability of occurrence of each anticipated fault is determined. Based on the power deficit and the probability of occurrence of each of the anticipated faults, the power deficit probability distribution is established.

[0009] In one example, based on historical wind speed data and historical solar irradiance data of the target power system, a joint probability distribution of wind and solar power output is established, and multiple wind and solar power output scenarios are generated, including: Marginal probability distributions were fitted to the historical wind speed data and the historical light intensity data respectively to obtain the edge probability distributions of wind speed and light intensity. Based on the correlation between the historical wind speed data and the historical light intensity data, the marginal probability distributions of wind speed and light intensity are connected using the Copula function to obtain the joint probability distribution of wind speed and light intensity. Based on the joint probability distribution of wind speed and light intensity, multiple sets of wind speed samples and light intensity samples are obtained. Each wind speed sample and light intensity sample is converted into a corresponding wind power output and photovoltaic power output to obtain the multiple wind and solar power output scenarios.

[0010] In one example, the step involves selecting multiple collocation points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, performing transient time-domain simulations on the system operation scenarios corresponding to each collocation point to obtain the frequency stability index corresponding to each collocation point, and constructing a three-dimensional polynomial chaotic expansion surrogate model based on each collocation point and its corresponding frequency stability index, including: The three-dimensional parameter space is determined based on the power deficit range, wind power output range, and photovoltaic power output range of the target power system. The power deficit, wind power output, and photovoltaic output are normalized, and the multiple matching points are selected in the normalized three-dimensional parameter space. The power deficit, wind power output and photovoltaic power output corresponding to each of the aforementioned points are loaded into the transient simulation model of the target power system to obtain the frequency response curves corresponding to each of the aforementioned points. Extract the corresponding frequency stability index from each of the frequency response curves; the frequency stability index includes at least one of the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation. Based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, the polynomial expansion coefficients are determined, and the three-dimensional polynomial chaotic expansion proxy model is constructed.

[0011] In one example, the step of determining the polynomial expansion coefficients based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, and constructing the three-dimensional polynomial chaotic expansion proxy model, includes: The power deficit, wind power output, and photovoltaic power output are respectively mapped to the standard intervals corresponding to the preset orthogonal polynomial basis functions; Based on the tensor product of multiple univariate orthogonal polynomials, construct multidimensional orthogonal polynomial basis functions corresponding to the three-dimensional input parameters; Based on the frequency stability index corresponding to each collocation point, the multidimensional orthogonal polynomial basis function, and the Gaussian integral weight corresponding to each collocation point, determine the expansion coefficients corresponding to each multidimensional orthogonal polynomial basis function. Based on the multidimensional orthogonal polynomial basis functions and their corresponding expansion coefficients, an explicit mapping relationship is established between the three-dimensional input parameters and the frequency stability index, thus obtaining the three-dimensional polynomial chaotic expansion surrogate model.

[0012] In one example, the process of obtaining multiple power deficit samples based on the power deficit probability distribution, combining each power deficit sample with multiple wind and solar power output scenarios to obtain multiple joint scenarios, and using the three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario includes: Based on the power deficit probability distribution, the power deficit corresponding to each of the anticipated faults is discretely sampled to obtain the multiple power deficit samples. The multiple power deficit samples are combined with the multiple wind and solar power output scenarios to obtain the multiple joint scenarios that respectively include power deficit, wind power output and photovoltaic power output; By inputting the power deficit, wind power output, and photovoltaic power output in each of the aforementioned joint scenarios into the three-dimensional polynomial chaotic expansion surrogate model, the frequency stability index corresponding to each of the aforementioned joint scenarios is obtained.

[0013] In one example, the step of determining the limit-crossing result of each joint scenario based on the comparison result of the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, and performing joint probability weighting on the limit-crossing result based on the failure occurrence probability and the probability of the wind and light scene corresponding to each joint scenario, includes: The frequency stability index corresponding to each of the joint scenarios is compared with the corresponding preset security threshold to determine the over-limit indication value corresponding to each of the joint scenarios. Based on the failure probability corresponding to the power deficit sample included in each joint scenario and the wind and solar scenario probability corresponding to the wind and solar power output scenario, the joint probability weight corresponding to each joint scenario is determined. The frequency over-limit risk of the target power system is obtained by summing the products of the over-limit indication values ​​corresponding to each joint scenario and the joint probability weights.

[0014] Secondly, the present invention also provides a power system frequency stability probability assessment system, the system comprising: The power deficit probability determination module is used to determine the power deficit and its probability of occurrence for each anticipated fault based on the anticipated fault set of the target power system, and to establish a power deficit probability distribution. The power output scenario generation module is used to establish a joint probability distribution of wind and solar power output based on the historical wind speed data and historical solar intensity data of the target power system, and generate multiple wind and solar power output scenarios. The proxy model construction module is used to take the power deficit, wind power output and photovoltaic output as three-dimensional input parameters, select multiple collocation points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, perform transient time-domain simulation on the system operation scenario corresponding to each collocation point, obtain the frequency stability index corresponding to each collocation point, and construct a three-dimensional polynomial chaotic expansion proxy model based on each collocation point and its corresponding frequency stability index. The stability index determination module is used to obtain multiple power deficit samples based on the power deficit probability distribution, combine each power deficit sample with the multiple wind and solar power output scenarios to obtain multiple joint scenarios, and use the three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario. The frequency limit exceedance risk determination module is used to determine the frequency limit exceedance result of each joint scenario based on the comparison result between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, and to perform joint probability weighting on the frequency limit exceedance result based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario to obtain the frequency limit exceedance risk of the target power system.

[0015] Thirdly, the present invention also provides an electronic device, the electronic device including a memory and a processor, the memory storing a computer program, the computer program being executed by the processor causing the processor to perform the steps of the power system frequency stability probability assessment method as described in the first aspect.

[0016] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed, implements the steps of the power system frequency stability probability assessment method as described in the first aspect.

[0017] As can be seen from the above technical solutions, this invention probabilistically models the power deficit and probability of occurrence corresponding to anticipated faults, and establishes correlated wind and solar power output scenarios by combining historical wind speed and solar irradiance. It unifies power deficit, wind power output, and solar power output as three-dimensional input parameters, and constructs a three-dimensional polynomial chaotic expansion surrogate model using transient time-domain simulation results with finite collocation points. This allows for the rapid determination of frequency stability indicators under various combined scenarios without repeatedly performing time-domain simulations for each wind-solar combination scenario under numerous faults. Simultaneously, by jointly weighting the frequency stability indicator exceedance results with the corresponding fault occurrence probability and wind-solar scenario probability, it can obtain frequency exceedance risks that simultaneously reflect the differences in fault types and the impact of new energy power output fluctuations. Therefore, this method reduces the computational load of frequency stability probability assessment, improves assessment efficiency, expands the coverage of uncertainty factors, and avoids incomplete risk information caused by assessing only fixed faults or single new energy power output conditions. This makes the obtained assessment results more reflective of the comprehensive frequency security risks that the target power system may face in actual operation, thus improving the accuracy of frequency stability assessment. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is an application environment diagram of a power system frequency stability probability assessment method provided in an embodiment of the present invention; Figure 2 A flowchart of a power system frequency stability probability assessment method provided in an embodiment of the present invention; Figure 3 A schematic diagram of the structure of a power system frequency stability probability assessment system provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The power system frequency stability probability assessment method provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 101 communicates with server 102 via a network. A data storage system can store the data that server 102 needs to process. The data storage system can be integrated onto server 102 or placed on a cloud or other network server. Terminal 101 or server 102 executes a power system frequency stability probability assessment method, which includes: determining the power deficit and probability of occurrence corresponding to each anticipated fault based on the anticipated fault set of the target power system, and establishing a power deficit probability distribution; establishing a joint probability distribution of wind and solar power output based on historical wind speed data and historical solar irradiance data of the target power system, and generating multiple wind and solar power output scenarios; using power deficit, wind power output, and solar power output as three-dimensional input parameters, selecting multiple points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, performing transient time-domain simulations on the system operation scenarios corresponding to each point, and obtaining the frequency stability index corresponding to each point. A three-dimensional polynomial chaotic expansion surrogate model is constructed based on each power distribution point and its corresponding frequency stability index. Multiple power deficit samples are obtained based on the power deficit probability distribution. Each power deficit sample is combined with multiple wind and solar power output scenarios to obtain multiple joint scenarios. The three-dimensional polynomial chaotic expansion surrogate model is used to determine the frequency stability index corresponding to each joint scenario. Based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, the over-limit result of each joint scenario is determined. Based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario, the over-limit result is weighted by joint probability to obtain the frequency over-limit risk of the target power system.

[0022] Terminal 101 can be, but is not limited to, various personal computers, laptops, smartphones, and tablets.

[0023] Server 102 can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server that provides cloud computing services.

[0024] In this embodiment, the target power system can be a regional power system including synchronous generator sets, wind farms, photovoltaic power plants, DC transmission systems, AC tie lines, and various loads, or it can be an interconnected grid or local grid that requires frequency security verification. The system data of the target power system may include grid topology data, generator set operation data, wind farm and photovoltaic power plant installed capacity and operation data, DC transmission power, tie line transmission power, load level, and dynamic parameters of governors, excitation systems, and new energy control systems.

[0025] like Figure 2As shown in the embodiments of this application, a method for probabilistic assessment of power system frequency stability is provided, which is applied to... Figure 1 Taking terminal 101 or server 102 as an example, the explanation includes the following steps S1 to S5. Wherein: Step S1: Based on the expected fault set of the target power system, determine the power deficit and occurrence probability corresponding to each expected fault, and establish the power deficit probability distribution.

[0026] In this embodiment, the anticipated fault set refers to the set of faults that are predetermined according to the safety verification requirements of the target power system and may cause an imbalance in the active power of the system and affect the frequency stability.

[0027] Anticipated faults can include at least one of the following: tripping of a single generator unit, single-pole blocking of the DC transmission system, double-pole blocking of the DC transmission system, and tripping of a critical tie line. Different anticipated faults result in different active power losses, and therefore the corresponding power deficits and their impact on system frequency also differ. By uniformly converting different types of anticipated faults into power deficits, the same input parameter can be used to characterize the impact of different faults on the system's active power balance. The probability of fault occurrence can be determined based on historical fault statistics.

[0028] Step S2: Based on the historical wind speed data and historical solar intensity data of the target power system, establish a joint probability distribution of wind and solar power output and generate multiple wind and solar power output scenarios.

[0029] Historical wind speed data can be a time series of wind speeds collected by wind farms or meteorological stations within the target area during a preset historical period, while historical solar irradiance data can be a time series of solar irradiance collected by photovoltaic power stations or meteorological stations within the target area during the same historical period. To ensure comparability between the two types of data, historical wind speed data and historical solar irradiance data can be organized using the same time resolution and the same time label.

[0030] The joint probability of wind and solar power output refers to the probability that wind power output and solar power output are simultaneously within a specific range. Since wind speed and solar intensity are correlated, the joint probability distribution cannot be obtained by simply multiplying the individual probability distributions of the two variables. Therefore, the correlation between the two is described by the Copula function. After constructing the joint probability distribution of wind and solar power output, multiple wind and solar power output scenarios that can reflect the actual probability characteristics can be generated by Monte Carlo sampling. These scenarios can then be combined with power deficit samples for the quantitative calculation of frequency stability risk.

[0031] Step S3: Using power deficit, wind power output, and photovoltaic output as three-dimensional input parameters, select multiple collocation points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, perform transient time-domain simulation on the system operation scenario corresponding to each collocation point, obtain the frequency stability index corresponding to each collocation point, and construct a three-dimensional polynomial chaotic expansion surrogate model based on each collocation point and its corresponding frequency stability index.

[0032] In this approach, power deficit is set as an input parameter alongside wind power output and photovoltaic output. This allows different fault types to be directly incorporated into the proxy model through the power deficit dimension, rather than being enumerated in an external loop outside the three-dimensional proxy model.

[0033] The three-dimensional parameter space is a continuous space spanned by the respective value ranges of the three-dimensional input parameters. Each point corresponds to a specific combination of power deficit, wind power output, and photovoltaic power output.

[0034] When selecting collocation points, Gaussian collocation points of corresponding orthogonal polynomials can be selected based on the probability distribution characteristics of each input parameter. This reduces the number of collocation points while covering the complete parameter space, thereby reducing the number of calculations in transient simulation and improving the efficiency of surrogate model construction.

[0035] Transient time-domain simulation accurately obtains the change process of system frequency over time after a fault occurs by performing time-domain simulation of the dynamic process of the target power system, and then extracts the frequency stability index of the corresponding matching point to ensure the calculation accuracy of the surrogate model.

[0036] The three-dimensional polynomial chaotic expansion surrogate model is a surrogate model that explicitly represents the mapping relationship between input parameters and frequency stability index through polynomial expansion. Compared with traditional nonlinear fitting methods, it has stronger adaptability to the probability distribution of input parameters, higher computational accuracy and efficiency, and can obtain high-precision output prediction results with only a small number of simulation points.

[0037] Step S4: Obtain multiple power deficit samples based on the power deficit probability distribution, combine each power deficit sample with multiple wind and solar power output scenarios to obtain multiple joint scenarios, and use a three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario.

[0038] When the power deficit probability distribution is a discrete probability distribution, the power deficit can be discretely sampled according to the probability of occurrence of each anticipated fault to obtain multiple power deficit samples. Alternatively, all power deficit values ​​in the anticipated fault set can be directly retained, and the corresponding fault occurrence probability can be used as the probability weight of the corresponding power deficit.

[0039] When the power deficit probability distribution is a continuous probability distribution, simple random sampling or importance sampling can be performed based on the corresponding probability density function to obtain multiple power deficit samples. Each power deficit sample has a corresponding probability weight.

[0040] Subsequently, each power deficit sample is combined with multiple wind and solar power output scenarios to form multiple joint scenarios containing three types of random parameters: power deficit, wind power output, and solar power output. Each joint scenario corresponds to a unique set of values ​​for the three types of parameters. At the same time, the probability of occurrence of the joint scenario can be directly calculated based on the probability of the power deficit sample and the probability of the corresponding wind and solar power output scenario.

[0041] Compared to the traditional hierarchical computational structure that enumerates faults and then traverses scenic scenes, this method of directly combining scenarios to obtain joint scenarios is more compatible with the input format of the three-dimensional polynomial chaotic expansion surrogate model, significantly simplifying the subsequent evaluation process. After obtaining all joint scenarios, the three types of parameters for each joint scenario are directly input into the pre-built three-dimensional polynomial chaotic expansion surrogate model, which can quickly calculate the frequency stability index corresponding to the joint scenario. There is no need to perform time-consuming transient time-domain simulations for each joint scenario, greatly reducing the overall computational load of the evaluation process.

[0042] Step S5: Based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, determine the over-limit result of each joint scenario, and perform joint probability weighting on the over-limit result according to the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario to obtain the frequency over-limit risk of the target power system.

[0043] The preset safety threshold is a frequency safety limit set in advance according to the system frequency stability control requirements. If the frequency stability index corresponding to a certain joint scenario exceeds the safety threshold, it is determined that there is a risk of frequency exceeding the limit in the joint scenario and it is marked as 1; otherwise, it is determined that there is no risk of frequency exceeding the limit and it is marked as 0.

[0044] The labeling result of each joint scenario is then multiplied by the product of the probability of failure and the probability of wind and solar scenarios corresponding to that joint scenario. The results of all joint scenarios are then summed. The final sum is the total frequency over-limit risk of the target power system. The larger this value is, the higher the probability of frequency over-limit occurring in the target power system and the worse the frequency stability level.

[0045] This application uses probabilistic modeling to model the power deficit and probability of occurrence corresponding to anticipated faults, and establishes correlated wind and solar power output scenarios by combining historical wind speed and solar irradiance. Power deficit, wind power output, and solar power output are unified as three-dimensional input parameters. A three-dimensional polynomial chaotic expansion surrogate model is constructed using transient time-domain simulation results with finite collocation points. This allows for the rapid determination of frequency stability indices under various combined scenarios without repeatedly performing time-domain simulations for each wind-solar combination scenario under numerous faults. Furthermore, by jointly weighting the frequency stability index exceedance results with the corresponding fault occurrence probability and wind-solar scenario probability, the frequency exceedance risk, reflecting both fault type differences and the impact of renewable energy output fluctuations, can be obtained. Therefore, this method reduces the computational burden of frequency stability probability assessment, improves assessment efficiency, expands the coverage of uncertainty factors, and avoids incomplete risk information caused by assessing only fixed faults or single renewable energy output conditions. The resulting assessment better reflects the comprehensive frequency security risks that the target power system may face in actual operation, thus improving the accuracy of frequency stability assessment.

[0046] In some embodiments, based on the set of anticipated faults of the target power system, determining the power deficit and probability of occurrence corresponding to each anticipated fault, and establishing a power deficit probability distribution, includes: determining a set of anticipated faults including multiple anticipated faults according to the safety verification requirements of the target power system; determining the power deficit corresponding to each anticipated fault according to the actual operating power of the transmission channel corresponding to each anticipated fault before its occurrence; determining the probability of occurrence of each anticipated fault according to the historical fault statistics of each anticipated fault; and establishing a power deficit probability distribution based on the power deficit and probability of occurrence corresponding to each anticipated fault.

[0047] Safety verification requirements can include N-1 safety verification requirements and N-2 safety verification requirements. The set of anticipated failures can be represented as:

[0048] in, Indicates the first An anticipated malfunction Indicates the number of anticipated failures. .

[0049] Anticipated faults can include at least one of the following: tripping of a single generator unit, single-pole blocking of the DC transmission system, double-pole blocking of the DC transmission system, and tripping of a critical tie line. Different anticipated faults result in different active power losses, and therefore the corresponding power deficits and their impact on system frequency also differ. By uniformly converting different types of anticipated faults into power deficits, the same input parameter can be used to characterize the impact of different faults on the system's active power balance.

[0050] Power deficit refers to the instantaneous reduction or transfer of active power in the target power system after a anticipated fault occurs, relative to the system's operating state before the fault. For the first... An anticipated malfunction The corresponding power deficit is denoted as The unit can be MW.

[0051] When the anticipated fault is generator tripping, the power deficit is... This can be determined as the actual output of the generator set before the fault occurred, i.e.:

[0052] in, Indicates the first The actual active power output of the generator set before tripping for a anticipated fault. Using actual output instead of rated capacity can avoid overestimating the power deficit when the generator set is not operating at full load.

[0053] When the anticipated fault is a DC transmission system shutdown, the power deficit... It can be determined as the transmission power of the corresponding DC transmission system before the blocking occurs, that is:

[0054] in, This represents the active power transmitted by the DC transmission system to the target power system before the blocking occurs.

[0055] When the anticipated fault is a tripping of a critical tie line, power deficit occurs. It can be determined that the transmission power of the corresponding tie line before the trip occurred, that is:

[0056] in, This indicates the active power transmitted by the tie line before the fault occurred.

[0057] The probability of occurrence of each anticipated fault is denoted as . The probability of a failure can be determined based on historical failure statistics. Specifically, it can be calculated based on the number of failures within a preset statistical period. Number of times a anticipated failure occurs and the total number of anticipated failures. And determine according to the following formula:

[0058] in, Indicates faults within the preset statistical period The number of times it occurs, This indicates the total number of anticipated failures that occurred within the statistical period.

[0059] In another implementation, the probability of a fault can also be determined based on equipment reliability parameters. For example, the probability of a corresponding anticipated fault can be determined based on the forced outage rate of the generator set, the reliability parameters of the DC transmission system, or the fault rate of the transmission line.

[0060] In another implementation, the probability of a fault can be dynamically adjusted by combining online equipment monitoring data and meteorological early warning information. Online equipment monitoring data may include generator vibration data, temperature data, and insulation status data; meteorological early warning information may include typhoon warnings, lightning warnings, or icing warnings. When the equipment's operating condition deteriorates or the external environment increases the likelihood of a fault, a Bayesian update method can be used to correct the initial probability of the corresponding fault, ensuring that the power deficit probability distribution matches the current operating state.

[0061] Based on the power deficit corresponding to each anticipated fault and probability of failure Discrete power deficit probability distributions can be established:

[0062] Among them, random variables Used to indicate the potential power deficit that the target power system may suffer. Represents the first... Each discrete value.

[0063] In practical engineering applications, a core set of anticipated faults can be formed by selecting critical faults that pose a significant threat to the frequency security of the target power system. For example, faults such as large-capacity generator tripping, DC blocking, and high-power tie-line tripping can be selected from all safety verification faults to form a set of anticipated faults containing multiple critical faults. For such a limited set of anticipated faults, a discrete probability distribution can be directly used to represent the power deficit.

[0064] When the number of anticipated faults is large, or when the power deficit needs to be treated as a continuous random variable, kernel density estimation or Gaussian mixture models can be used to analyze the power deficit samples. By fitting the data, a continuous power deficit probability density function is obtained. This allows for continuous sampling of the power deficit while preserving the probability characteristics of different fault sizes.

[0065] In some embodiments, based on historical wind speed data and historical solar intensity data of the target power system, a joint probability distribution of wind and solar power output is established, and multiple wind and solar power output scenarios are generated. This includes: fitting the historical wind speed data and historical solar intensity data with marginal probability distributions to obtain wind speed marginal probability distributions and solar intensity marginal probability distributions; connecting the wind speed marginal probability distribution and solar intensity marginal probability distribution using a Copula function based on the correlation between the historical wind speed data and historical solar intensity data to obtain a joint probability distribution of wind speed and solar intensity; sampling based on the joint probability distribution of wind speed and solar intensity to obtain multiple sets of wind speed samples and solar intensity samples; and converting each wind speed sample and solar intensity sample into corresponding wind power output and solar power output to obtain multiple wind and solar power output scenarios.

[0066] Marginal probability distribution refers to a probability distribution that describes only the statistical characteristics of a single random variable. First, a marginal probability distribution is fitted to the historical wind speed data. In this embodiment, a two-parameter Weibull distribution can be used to fit the wind speed probability distribution, and its probability density function is:

[0067] in, This is the wind speed value. For scale parameters, For shape parameters. For scale parameters. Used to reflect the overall level of wind speed, shape parameters It is used to reflect the distribution pattern of wind speed. The scale parameter and shape parameter can be determined based on historical wind speed data using the maximum likelihood estimation method.

[0068] For historical light intensity data, a two-parameter Beta distribution can be used to fit its probability distribution, and its probability density function is:

[0069] in, This represents the light intensity value. This represents the maximum light intensity within the corresponding time period. and For shape parameters, This is the Gamma function. Parameters and It can be determined based on historical light intensity data using the maximum likelihood estimation method.

[0070] Since wind speed and light intensity are not completely independent, sampling them separately may not preserve the actual wind-solar complementarity in the target area. Therefore, after obtaining the marginal probability distributions of wind speed and light intensity, it is necessary to use the Copula function to establish their joint probability distribution.

[0071] The Copula function is used to connect the marginal probability distributions of multiple random variables into a joint probability distribution and independently describe the correlation structure between the random variables. In this embodiment, the Frank-Copula function can be used to describe the correlation between wind speed and light intensity.

[0072] First, Kendall's rank correlation coefficient is calculated based on historical wind speed data and historical light intensity data with the same time label. Then, based on the Kendall rank correlation coefficient and the Frank-Copula parameters... The analytical relationship between them determines the parameters. The joint distribution function of wind speed and light intensity is:

[0073] in: This represents the edge cumulative distribution function of wind speed. This represents the edge cumulative distribution function of light intensity. Through the above processing, the correlation between wind speed and light intensity can be maintained while preserving their respective edge statistical characteristics.

[0074] Based on the joint probability distribution of wind speed and light intensity, it is possible to perform... Sub-Monte Carlo sampling yielded:

[0075] in, Indicates the first Group of wind speed samples, Indicates the first Group of light intensity samples, The value can be determined based on the required accuracy of the probability assessment; for example, it can be between 5,000 and 10,000.

[0076] Then, the meteorological samples are converted into wind power output and photovoltaic power output. For wind power output, the conversion can be performed based on the power-wind speed characteristic curve of the wind turbine. A typical segmented relationship is as follows:

[0077] in, Wind speed The corresponding wind power output, To cut into wind speed, To cut off the wind speed, air density, Where is the radius of the wind turbine. The maximum wind energy utilization factor, This refers to the rated power of the wind turbine.

[0078] For photovoltaic output, under maximum power point tracking control, the relationship between irradiance and photovoltaic output can be approximately satisfied as follows:

[0079] in, Indicates light intensity The corresponding photovoltaic output, This indicates the overall conversion efficiency of the photovoltaic array. Indicates the effective light-receiving area. This indicates the rated capacity of the photovoltaic array.

[0080] After performing the above transformation on each set of wind speed and light intensity samples, we can obtain:

[0081] Each group This creates a scenic and productive scene.

[0082] This application, by simultaneously preserving the edge probability characteristics and correlations of wind speed and solar intensity, can avoid scenarios that do not conform to actual meteorological patterns due to the independent generation of wind power output and solar power output, and provide wind and solar power output inputs with actual statistical characteristics for subsequent frequency risk assessment.

[0083] In some embodiments, multiple collocation points are selected in the three-dimensional parameter space corresponding to the three-dimensional input parameters. Transient time-domain simulations are performed on the system operation scenarios corresponding to each collocation point to obtain the frequency stability index corresponding to each collocation point. A three-dimensional polynomial chaotic expansion proxy model is constructed based on each collocation point and its corresponding frequency stability index. This includes: determining the three-dimensional parameter space based on the power deficit range, wind power output range, and photovoltaic output range of the target power system; normalizing the power deficit, wind power output, and photovoltaic output, and selecting multiple collocation points in the normalized three-dimensional parameter space; loading the power deficit, wind power output, and photovoltaic output corresponding to each collocation point into the transient simulation model of the target power system to obtain the frequency response curve corresponding to each collocation point; extracting the corresponding frequency stability index from each frequency response curve; the frequency stability index includes at least one of the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation; determining the polynomial expansion coefficients based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, and constructing a three-dimensional polynomial chaotic expansion proxy model.

[0084] Specifically, based on each collocation point, its corresponding frequency stability index, and pre-defined orthogonal polynomial basis functions, polynomial expansion coefficients are determined, and a three-dimensional polynomial chaotic expansion surrogate model is constructed. This includes: mapping power deficit, wind power output, and photovoltaic power output to the standard intervals corresponding to the pre-defined orthogonal polynomial basis functions; constructing multidimensional orthogonal polynomial basis functions corresponding to the three-dimensional input parameters based on the tensor product of multiple univariate orthogonal polynomials; determining the expansion coefficients corresponding to each multidimensional orthogonal polynomial basis function based on the frequency stability index corresponding to each collocation point, the multidimensional orthogonal polynomial basis functions, and the Gaussian integral weights corresponding to each collocation point; and establishing an explicit mapping relationship between the three-dimensional input parameters and the frequency stability index based on the multidimensional orthogonal polynomial basis functions and their corresponding expansion coefficients, thus obtaining the three-dimensional polynomial chaotic expansion surrogate model.

[0085] In this embodiment, the three-dimensional input parameters can be expressed as:

[0086] in, This indicates the power deficit caused by the fault. Indicates wind power output. This represents photovoltaic output. By setting the power deficit as an input parameter alongside wind and photovoltaic output, different fault types are no longer enumerated in an external loop of the three-dimensional proxy model, but are directly incorporated into the proxy model through the power deficit dimension.

[0087] The transient frequency response of the target power system under high-power disturbance can be represented as a system of differential-algebraic equations with three-dimensional input parameters:

[0088] in, This is a vector of system state variables, which may include synchronous generator rotor angle, rotor speed, and control system state variables. The system is a vector of algebraic variables, which may include bus voltage magnitude, bus voltage phase angle, and line power flow, etc. Represents the function vector of a differential equation; A vector representing a function in an algebraic equation.

[0089] Given input parameters In this case, by solving the above differential-algebraic equations, the corresponding system frequency response and frequency stability index can be obtained. Frequency stability index The following implicit relationship exists between the three-dimensional input parameters and the parameters:

[0090] Since this implicit relationship needs to be solved through transient time-domain simulation, this embodiment establishes a corresponding explicit proxy model through polynomial chaotic expansion to reduce repetitive time-domain simulations in a large number of joint scenarios.

[0091] The three-dimensional parameter space can be represented as:

[0092] in, and These represent the minimum and maximum power deficit, respectively. and These represent the minimum and maximum values ​​of wind power output, respectively. and These represent the minimum and maximum values ​​of photovoltaic output, respectively.

[0093] The power deficit range can extend from zero to the maximum power deficit the target power system may experience. The maximum power deficit can be determined based on the actual output of the largest single generator unit in the target power system, the maximum DC transmission power, or the power loss corresponding to other critical faults. Wind power output and photovoltaic output can be determined according to the range from zero output to rated output of the corresponding renewable energy plants, and can be normalized to a range. .

[0094] To employ predefined orthogonal polynomial basis functions, power deficit, wind power output, and photovoltaic power output can be mapped to corresponding standard intervals. For example, when using Legendre polynomials as orthogonal polynomial basis functions, linear transformations can be used to map each input parameter to an interval. .

[0095] After determining and normalizing the parameter space, the collocation points can be generated using the three-dimensional tensor product method. For polynomial approximation orders... Select on each input dimension The number of Gaussian integral nodes is then combined with tensor products on the nodes of the three input dimensions to obtain the number of collocation points:

[0096] in, This indicates the total number of points.

[0097] In a preferred embodiment, the order of the polynomial approximation is taken as... At this point, selecting four nodes in each of the three dimensions of power deficit, wind power output, and photovoltaic power output, we can obtain the following through tensor product:

[0098] One point. Each collocation point can be represented as:

[0099] For each power distribution point, its corresponding power deficit, wind power output, and photovoltaic output are loaded into the transient simulation model of the target power system. When loading the power deficit, the corresponding scale of active power loss can be simulated at the time of the preset fault occurrence; when loading the wind power output and photovoltaic output, the active power output of the renewable energy power station before the fault occurs can be adjusted so that the initial operating state of the simulation model matches the wind and solar output corresponding to the power distribution point.

[0100] A complete transient time-domain simulation is performed for each collocation point to obtain the system frequency response curve as the frequency changes over time. Then, at least one of the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation is extracted from the frequency response curve.

[0101] The initial rate of change of frequency can be expressed as:

[0102] in, Indicates the system frequency. This indicates the initial time after the power disturbance occurs. The initial frequency change rate reflects how quickly the system's frequency changes after the power disturbance occurs, and it is closely related to the system's equivalent inertia and the magnitude of the power deficit.

[0103] The maximum frequency deviation can be expressed as:

[0104] in, This indicates the deviation of the system frequency from the rated frequency. The maximum frequency deviation reflects the greatest extent to which the frequency deviates from the rated frequency throughout the entire transient process.

[0105] The quasi-steady-state frequency deviation can be expressed as:

[0106] The quasi-steady-state frequency deviation reflects the deviation of the system frequency from the rated frequency after a single frequency modulation process. In finite-duration simulations, the corresponding quasi-steady-state frequency deviation can be determined from the time interval during which the frequency response curve enters a relatively stable state, but its definition still follows the formula above.

[0107] Therefore, the input-output data pairs corresponding to each collocation point can be obtained:

[0108] in, These can correspond to the initial frequency change rate, the maximum frequency deviation, and the quasi-steady-state frequency deviation, respectively.

[0109] In this embodiment, a three-dimensional polynomial chaotic expansion surrogate model can be constructed for different frequency stability indices. The preset orthogonal polynomial basis functions can be three-dimensional Legendre polynomial basis functions. For the three-dimensional input parameters... , No. A multidimensional orthogonal polynomial basis function can be constructed from the tensor product of three univariate Legendre polynomials:

[0110] in, , and These represent the univariate polynomial orders corresponding to the three input dimensions: power deficit, wind power output, and photovoltaic power output, respectively.

[0111] The recurrence relation for a single-variable Legendre polynomial is:

[0112] When the total order When the term is , the number of terms in the basis functions of the three-dimensional orthogonal polynomial is:

[0113] No. The polynomial chaotic expansion approximation expression for each frequency stability index is:

[0114] in, Indicates the first The output value of the proxy model for a frequency stability index. Indicates the first The frequency stability index corresponding to the first One expansion coefficient.

[0115] Each expansion coefficient can be calculated based on the frequency stability index at the collocation point, the orthogonal polynomial basis function values, and the Gaussian integral weights:

[0116] in: Indicates the first The Gaussian integral weights corresponding to each collocation point The first term obtained through transient time-domain simulation is represented as... The true value of the frequency stability index at each matching point.

[0117] Based on all expansion coefficients and multidimensional orthogonal polynomial basis functions, an explicit mapping relationship between power deficit, wind power output, photovoltaic power output and frequency stability index can be obtained.

[0118] Furthermore, after completing the proxy model construction, it is also possible to perform [further analysis] in the three-dimensional parameter space. Multiple test points, distinct from the points mentioned above, are randomly selected. For each test point, a frequency stability index is calculated using a three-dimensional polynomial chaotic expansion surrogate model, while a transient time-domain simulation is performed to obtain the true value of the corresponding index. The relative error between the two is then compared.

[0119] When the mean relative error meets the preset engineering accuracy requirements, the surrogate model can be used for subsequent probability assessments. For example, the preset engineering accuracy requirement can be a mean relative error of less than 5%. When the surrogate model's accuracy does not meet the requirements, the approximation order can be increased to... The number of points to be allocated at this time is:

[0120] The number of basis function terms is:

[0121] Then re-execute the collocation simulation and build the surrogate model.

[0122] In other implementations, when further considering load uncertainty, unit combination status, or other input factors that lead to an increase in parameter dimension, a sparse grid method can be used to select points to reduce the number of points in the high-dimensional parameter space.

[0123] In other implementations, Gaussian process regression or radial basis function interpolation can be used to construct a surrogate model for the frequency stability index. Such surrogate models can also establish an explicit mapping relationship between the three-dimensional input parameters and the frequency stability index using a limited number of collocational simulation data.

[0124] Furthermore, the orthogonal polynomial basis functions can be selected based on the probability distribution of the input parameters. For example, Jacobi polynomials can be used for input parameters with Beta distribution characteristics, while Hermite polynomials can be used for input parameters with normal distribution characteristics. These alternative methods can be used to improve approximation efficiency under specific probability distribution conditions, but in this embodiment, three-dimensional Legendre polynomials are preferred for constructing the surrogate model.

[0125] This application only requires performing transient time-domain simulations at a limited number of coordinate points to establish an explicit surrogate model covering the entire three-dimensional parameter space. In subsequent evaluations, for any combination of power deficit, wind power output, and photovoltaic power output, only polynomial evaluation is required, without needing to perform a complete transient time-domain simulation again.

[0126] In some embodiments, multiple power deficit samples are obtained based on the power deficit probability distribution. Each power deficit sample is combined with multiple wind and solar power output scenarios to obtain multiple joint scenarios. A three-dimensional polynomial chaotic expansion surrogate model is used to determine the frequency stability index corresponding to each joint scenario. This includes: discretely sampling the power deficit corresponding to each anticipated fault according to the power deficit probability distribution to obtain multiple power deficit samples; combining the multiple power deficit samples with multiple wind and solar power output scenarios to obtain multiple joint scenarios that respectively include power deficit, wind power output, and solar power output; and inputting the power deficit, wind power output, and solar power output in each joint scenario into a three-dimensional polynomial chaotic expansion surrogate model to obtain the frequency stability index corresponding to each joint scenario.

[0127] Specifically, let the number of power deficit samples be... The number of landscape output scenes is The power deficit samples can be combined with the wind and solar power output scenarios using a Cartesian product to obtain:

[0128] A joint scenario. The power deficit sample and the first The combined scene formed by the individual scenic output scenes can be represented as:

[0129] in, , .

[0130] For example, for a power deficit sample They can be compared with all of them. A combination of wind and solar power output scenarios is used to evaluate the frequency response of the power deficit under different wind and solar operating conditions; for another power deficit sample, the above combination process is repeated. In this way, multiple combinations of fault scale and wind and solar operating conditions can be covered without performing transient time-domain simulations for each combination.

[0131] Substituting the power deficit, wind power output, and photovoltaic output of each joint scenario into the three-dimensional polynomial chaotic expansion surrogate model constructed in step S3, we can obtain the following:

[0132] in, Indicates the joint scenario number.

[0133] The above calculation process only involves evaluating orthogonal polynomial basis functions and weighted summation of expansion coefficients, resulting in a significantly lower computational cost compared to transient time-domain simulation. Therefore, even with tens of thousands or more joint scenarios, frequency stability indices for all scenarios can be obtained in a relatively short time.

[0134] In some embodiments, the frequency stability index corresponding to each joint scenario is compared with the corresponding preset safety threshold to determine the over-limit result of each joint scenario, and the over-limit result is weighted by joint probability based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario. This includes: comparing the frequency stability index corresponding to each joint scenario with the corresponding preset safety threshold to determine the over-limit indication value corresponding to each joint scenario; determining the joint probability weight corresponding to each joint scenario based on the fault occurrence probability corresponding to the power deficit sample included in each joint scenario and the wind and solar scenario probability corresponding to the wind and solar power output scenario; and summing the product of the over-limit indication value corresponding to each joint scenario and the joint probability weight to obtain the frequency over-limit risk of the target power system.

[0135] For the The first joint scenario and the first A frequency stability index can define an over-limit indicator function. The original method for determining whether a limit was exceeded was as follows: For frequency stability indices with upper limit constraints, the over-limit indicator value is set to 1 when the following formula is satisfied:

[0136] For frequency stability indices with lower limit constraints, the over-limit indication value is set to 1 when the following formula is satisfied:

[0137] When the corresponding frequency stability index does not exceed the limit:

[0138] in, Indicates the first The first joint scenario corresponds to the first One frequency stability indicator, This indicates the preset safety threshold corresponding to this indicator.

[0139] Joint probability weights are used to characterize the likelihood of a certain joint scenario occurring. For the first... The power deficit sample and the first The joint probability weight of a combined scenario formed by several wind and solar power output scenarios can be determined based on the corresponding failure probability and the probability of the wind and solar power scenario.

[0140] When the wind and solar power output scenarios are directly sampled using a joint probability distribution via Monte Carlo sampling, and each scenario is represented with equal probability, the probability of each scenario can be taken as:

[0141] When the power deficit is represented by discrete fault probabilities, the first... The probability weight corresponding to each power deficit sample can be taken as the probability of the corresponding fault occurrence. Therefore, the first The power deficit sample and the first The probability weights of the joint scene formed by the individual landscape power output scenes can be expressed as:

[0142] For the The frequency stability index, and the risk of frequency exceeding the limit in the full probability sense, can be calculated using the following formula:

[0143] in, Indicates the first The frequency limit exceeding risk corresponds to each frequency stability indicator. Indicates the first The probability of fault occurrence corresponding to each power deficit sample This indicates the over-limit indication value for the corresponding joint scenario.

[0144] When power deficits are sampled according to a continuous probability distribution, each power deficit sample can be weighted equally, or the sample weights can be adjusted according to the corresponding probability density. When the scenic scene is not obtained through equal-probability Monte Carlo sampling, the actual probability of the corresponding scenic scene can also be used as the scenic scene probability.

[0145] For example, when the frequency stability index of a certain joint scenario exceeds the corresponding safety threshold, its over-limit indication value is 1, and the joint probability weight of that joint scenario will be included in the frequency over-limit risk; when no over-limit occurs in that joint scenario, its over-limit indication value is 0, and no corresponding frequency over-limit risk will be added. By summing the products of the joint probability weights of all joint scenarios and the over-limit indication values, the frequency over-limit risk that comprehensively considers the probability of different failures and different wind and solar operation states can be obtained.

[0146] Furthermore, kernel density estimation can be performed on the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation corresponding to all joint scenarios to obtain the probability density function of each frequency stability index under dual uncertainty.

[0147] Furthermore, the joint scenarios can be grouped according to different power deficits, and the frequency exceedance risk corresponding to each power deficit can be statistically analyzed to form a comparison result of frequency exceedance risk under different power deficits. This result can be used to identify critical faults that have a significant impact on the frequency security of the target power system.

[0148] The system can output the following evaluation results: probability density functions for each frequency stability index, frequency exceedance risk values ​​for each frequency stability index, and comparison results of frequency exceedance risks under different power deficits. These output results can be displayed in tables, probability density curves, or risk comparison charts.

[0149] In another implementation, when the power deficit is represented by a continuous probability density function, a three-dimensional polynomial chaotic expansion surrogate model can be combined with the power deficit probability density function and the joint probability density function of wind and solar power output. Triple numerical integration of the over-limit indicator function is then performed in the three-dimensional parameter space to directly calculate the frequency over-limit risk without explicitly generating a large number of joint scenarios. This approach is particularly suitable for cases with low-dimensional input parameters.

[0150] This application can not only obtain the probability of conditional overrun under a given fault, but also use the occurrence probability of different faults and the probability of wind and solar power scenarios to perform joint weighting, so as to obtain a comprehensive risk result that simultaneously reflects the uncertainty of fault type and the uncertainty of wind and solar power output.

[0151] Based on the same inventive concept, this application also provides a power system frequency stability probability assessment system for implementing the power system frequency stability probability assessment method described above.

[0152] The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more power system frequency stability probability assessment system embodiments provided below can be found in the limitations of the power system frequency stability probability assessment method described above, and will not be repeated here.

[0153] like Figure 3 As shown in the figure, this application provides a power system frequency stability probability assessment system, which includes: The power deficit probability determination module 100 is used to determine the power deficit and its probability of occurrence for each anticipated fault based on the anticipated fault set of the target power system, and to establish a power deficit probability distribution. The power output scenario generation module 200 is used to establish a joint probability distribution of wind and solar power output based on the historical wind speed data and historical solar intensity data of the target power system, and generate multiple wind and solar power output scenarios. The proxy model construction module 300 is used to take power deficit, wind power output and photovoltaic output as three-dimensional input parameters, select multiple collocation points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, perform transient time-domain simulation on the system operation scenario corresponding to each collocation point, obtain the frequency stability index corresponding to each collocation point, and construct a three-dimensional polynomial chaotic expansion proxy model based on each collocation point and its corresponding frequency stability index. The stability index determination module 400 is used to obtain multiple power deficit samples based on the power deficit probability distribution, combine each power deficit sample with multiple wind and solar power output scenarios to obtain multiple joint scenarios, and use a three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario. The frequency limit exceedance risk determination module 500 is used to determine the frequency limit exceedance result of each joint scenario based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold. Based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario, the frequency limit exceedance risk of the target power system is obtained by joint probability weighting of the frequency limit exceedance result.

[0154] In some embodiments, the shortage probability determination module 100 is used for: Based on the safety verification requirements of the target power system, a set of anticipated faults, including multiple anticipated faults, is determined; Based on the actual operating power of the transmission channel corresponding to each anticipated fault before its occurrence, determine the power deficit corresponding to each anticipated fault. Based on the historical failure statistics of each anticipated failure, determine the probability of occurrence of each anticipated failure. Based on the power deficit and the probability of occurrence of each anticipated fault, a power deficit probability distribution is established.

[0155] In some embodiments, the output scenario generation module 200 is used for: Marginal probability distributions were fitted to historical wind speed data and historical light intensity data respectively to obtain the marginal probability distributions of wind speed and light intensity. Based on the correlation between historical wind speed data and historical light intensity data, the Copula function is used to connect the marginal probability distributions of wind speed and light intensity to obtain the joint probability distribution of wind speed and light intensity. Sampling was performed based on the joint probability distribution of wind speed and light intensity to obtain multiple sets of wind speed samples and light intensity samples; Each wind speed sample and light intensity sample was converted into corresponding wind power output and photovoltaic power output to obtain multiple wind and solar power output scenarios.

[0156] In some embodiments, the agent model construction module 300 is used for: The three-dimensional parameter space is determined based on the power deficit range, wind power output range, and photovoltaic power output range of the target power system. The power deficit, wind power output, and photovoltaic output are normalized, and multiple matching points are selected in the normalized three-dimensional parameter space. The power deficit, wind power output and photovoltaic power output corresponding to each distribution point are loaded into the transient simulation model of the target power system to obtain the frequency response curves corresponding to each distribution point. Extract the corresponding frequency stability index from each frequency response curve; the frequency stability index includes at least one of the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation. Based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, the polynomial expansion coefficients are determined, and a three-dimensional polynomial chaotic expansion surrogate model is constructed.

[0157] In some embodiments, the agent model construction module 300 is used for: The power deficit, wind power output, and photovoltaic power output are respectively mapped to the standard intervals corresponding to the preset orthogonal polynomial basis functions; Based on the tensor product of multiple univariate orthogonal polynomials, construct multidimensional orthogonal polynomial basis functions corresponding to the three-dimensional input parameters; Based on the frequency stability index corresponding to each collocation point, the multidimensional orthogonal polynomial basis function, and the Gaussian integral weight corresponding to each collocation point, determine the expansion coefficients corresponding to each multidimensional orthogonal polynomial basis function. Based on the multidimensional orthogonal polynomial basis functions and their corresponding expansion coefficients, an explicit mapping relationship between the three-dimensional input parameters and the frequency stability index is established, resulting in a three-dimensional polynomial chaotic expansion surrogate model.

[0158] In some embodiments, the stability index determination module 400 is used for: Based on the power deficit probability distribution, the power deficit corresponding to each anticipated fault is discretely sampled to obtain multiple power deficit samples. By combining multiple power deficit samples with multiple wind and solar power output scenarios, multiple joint scenarios are obtained, which respectively include power deficit, wind power output and solar power output; By inputting the power deficit, wind power output, and photovoltaic power output in each joint scenario into a three-dimensional polynomial chaotic expansion proxy model, the frequency stability index corresponding to each joint scenario is obtained.

[0159] In some embodiments, the limit exceedance risk determination module 500 is used for: Compare the frequency stability index corresponding to each joint scenario with the corresponding preset security threshold to determine the over-limit indication value corresponding to each joint scenario. Based on the probability of fault occurrence corresponding to the power deficit sample included in each joint scenario and the probability of wind and solar power output scenario corresponding to the wind and solar power output scenario, the joint probability weight corresponding to each joint scenario is determined. The frequency over-limit risk of the target power system is obtained by summing the products of the over-limit indication values ​​corresponding to each joint scenario and the joint probability weights.

[0160] like Figure 4 As shown, this application provides an electronic device. The electronic device 10 includes a memory 20 and a processor 30. The memory 20 stores a computer program. When the computer program is executed by the processor 30, the processor 30 performs the steps of the power system frequency stability probability assessment method as described in the above embodiment.

[0161] This application provides a computer-readable storage medium storing a computer program thereon, which, when executed, implements the steps of the power system frequency stability probability assessment method as described in the above embodiments.

[0162] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, electronic devices, and computer storage media described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0163] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0164] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0165] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0166] In the embodiments provided by this invention, it should be understood that the disclosed systems, electronic devices, computer storage media, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0167] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0168] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0169] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for executing all or part of the steps of the methods described in the various embodiments of the present invention through a computer device (which may be a personal computer, a server, or a network device, etc.). The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0170] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for probabilistic assessment of frequency stability in a power system, characterized in that, The method includes: Based on the anticipated fault set of the target power system, determine the power deficit and occurrence probability corresponding to each anticipated fault, and establish the power deficit probability distribution. Based on the historical wind speed data and historical solar intensity data of the target power system, a joint probability distribution of wind and solar power output is established, and multiple wind and solar power output scenarios are generated. Using the power deficit, wind power output, and photovoltaic power output as three-dimensional input parameters, multiple collocation points are selected in the three-dimensional parameter space corresponding to the three-dimensional input parameters. Transient time-domain simulation is performed on the system operation scenario corresponding to each collocation point to obtain the frequency stability index corresponding to each collocation point. A three-dimensional polynomial chaotic expansion surrogate model is constructed based on each collocation point and its corresponding frequency stability index. Multiple power deficit samples are obtained based on the power deficit probability distribution. Each power deficit sample is combined with the multiple wind and solar power output scenarios to obtain multiple joint scenarios. The frequency stability index corresponding to each joint scenario is determined using the three-dimensional polynomial chaotic expansion surrogate model. Based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, the over-limit result of each joint scenario is determined. Then, based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario, the over-limit result is weighted by joint probability to obtain the frequency over-limit risk of the target power system.

2. The power system frequency stability probability assessment method according to claim 1, characterized in that, The process of determining the power deficit and probability of occurrence corresponding to each anticipated fault based on the set of anticipated faults of the target power system, and establishing a power deficit probability distribution, includes: Based on the safety verification requirements of the target power system, a set of anticipated faults, including multiple anticipated faults, is determined; Based on the actual operating power of the transmission channel corresponding to each of the anticipated faults before its occurrence, determine the power deficit corresponding to each of the anticipated faults. Based on the historical fault statistics of each of the aforementioned anticipated faults, the probability of occurrence of each anticipated fault is determined. Based on the power deficit and the probability of occurrence of each of the anticipated faults, the power deficit probability distribution is established.

3. The power system frequency stability probability assessment method according to claim 1, characterized in that, Based on historical wind speed and solar irradiance data of the target power system, a joint probability distribution of wind and solar power output is established, and multiple wind and solar power output scenarios are generated, including: Marginal probability distributions were fitted to the historical wind speed data and the historical light intensity data respectively to obtain the edge probability distributions of wind speed and light intensity. Based on the correlation between the historical wind speed data and the historical light intensity data, the marginal probability distributions of wind speed and light intensity are connected using the Copula function to obtain the joint probability distribution of wind speed and light intensity. Based on the joint probability distribution of wind speed and light intensity, multiple sets of wind speed samples and light intensity samples are obtained. Each wind speed sample and light intensity sample is converted into a corresponding wind power output and photovoltaic power output to obtain the multiple wind and solar power output scenarios.

4. The power system frequency stability probability assessment method according to claim 1, characterized in that, The process involves selecting multiple collocation points within the three-dimensional parameter space corresponding to the three-dimensional input parameters, performing transient time-domain simulations on the system operation scenarios corresponding to each collocation point, obtaining the frequency stability index corresponding to each collocation point, and constructing a three-dimensional polynomial chaotic expansion surrogate model based on each collocation point and its corresponding frequency stability index, including: The three-dimensional parameter space is determined based on the power deficit range, wind power output range, and photovoltaic power output range of the target power system. The power deficit, wind power output, and photovoltaic output are normalized, and the multiple matching points are selected in the normalized three-dimensional parameter space. The power deficit, wind power output and photovoltaic power output corresponding to each of the aforementioned points are loaded into the transient simulation model of the target power system to obtain the frequency response curves corresponding to each of the aforementioned points. Extract the corresponding frequency stability index from each of the frequency response curves; the frequency stability index includes at least one of the initial frequency change rate, maximum frequency deviation, and quasi-steady-state frequency deviation. Based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, the polynomial expansion coefficients are determined, and the three-dimensional polynomial chaotic expansion proxy model is constructed.

5. The power system frequency stability probability assessment method according to claim 4, characterized in that, The step of determining the polynomial expansion coefficients based on each collocation point, the corresponding frequency stability index, and the preset orthogonal polynomial basis functions, and constructing the three-dimensional polynomial chaotic expansion proxy model, includes: The power deficit, wind power output, and photovoltaic power output are respectively mapped to the standard intervals corresponding to the preset orthogonal polynomial basis functions; Based on the tensor product of multiple univariate orthogonal polynomials, construct multidimensional orthogonal polynomial basis functions corresponding to the three-dimensional input parameters; Based on the frequency stability index corresponding to each collocation point, the multidimensional orthogonal polynomial basis function, and the Gaussian integral weight corresponding to each collocation point, determine the expansion coefficients corresponding to each multidimensional orthogonal polynomial basis function. Based on the multidimensional orthogonal polynomial basis functions and their corresponding expansion coefficients, an explicit mapping relationship is established between the three-dimensional input parameters and the frequency stability index, thus obtaining the three-dimensional polynomial chaotic expansion surrogate model.

6. The power system frequency stability probability assessment method according to claim 1, characterized in that, The process involves obtaining multiple power deficit samples based on the power deficit probability distribution, combining each power deficit sample with multiple wind and solar power output scenarios to obtain multiple joint scenarios, and using the three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario, including: Based on the power deficit probability distribution, the power deficit corresponding to each of the anticipated faults is discretely sampled to obtain the multiple power deficit samples. The multiple power deficit samples are combined with the multiple wind and solar power output scenarios to obtain the multiple joint scenarios that respectively include power deficit, wind power output and photovoltaic power output; By inputting the power deficit, wind power output, and photovoltaic power output in each of the aforementioned joint scenarios into the three-dimensional polynomial chaotic expansion surrogate model, the frequency stability index corresponding to each of the aforementioned joint scenarios is obtained.

7. The power system frequency stability probability assessment method according to claim 1, characterized in that, The step involves determining the limit-crossing result of each joint scenario based on the comparison results between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, and then performing a joint probability weighting on the limit-crossing result based on the fault occurrence probability and the probability of the wind and light scene corresponding to each joint scenario, including: The frequency stability index corresponding to each of the joint scenarios is compared with the corresponding preset security threshold to determine the over-limit indication value corresponding to each of the joint scenarios. Based on the failure probability corresponding to the power deficit sample included in each joint scenario and the wind and solar scenario probability corresponding to the wind and solar power output scenario, the joint probability weight corresponding to each joint scenario is determined. The frequency over-limit risk of the target power system is obtained by summing the products of the over-limit indication values ​​corresponding to each joint scenario and the joint probability weights.

8. A power system frequency stability probability assessment system, characterized in that, The system includes: The power deficit probability determination module is used to determine the power deficit and its probability of occurrence for each anticipated fault based on the anticipated fault set of the target power system, and to establish a power deficit probability distribution. The power output scenario generation module is used to establish a joint probability distribution of wind and solar power output based on the historical wind speed data and historical solar intensity data of the target power system, and generate multiple wind and solar power output scenarios. The proxy model construction module is used to take the power deficit, wind power output and photovoltaic output as three-dimensional input parameters, select multiple collocation points in the three-dimensional parameter space corresponding to the three-dimensional input parameters, perform transient time-domain simulation on the system operation scenario corresponding to each collocation point, obtain the frequency stability index corresponding to each collocation point, and construct a three-dimensional polynomial chaotic expansion proxy model based on each collocation point and its corresponding frequency stability index. The stability index determination module is used to obtain multiple power deficit samples based on the power deficit probability distribution, combine each power deficit sample with the multiple wind and solar power output scenarios to obtain multiple joint scenarios, and use the three-dimensional polynomial chaotic expansion surrogate model to determine the frequency stability index corresponding to each joint scenario. The frequency limit exceedance risk determination module is used to determine the frequency limit exceedance result of each joint scenario based on the comparison result between the frequency stability index corresponding to each joint scenario and the corresponding preset safety threshold, and to perform joint probability weighting on the frequency limit exceedance result based on the fault occurrence probability and wind and solar scenario probability corresponding to each joint scenario to obtain the frequency limit exceedance risk of the target power system.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the steps of the power system frequency stability probability assessment method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the steps of the power system frequency stability probability assessment method as described in any one of claims 1-7.

Images