Global sensitivity calculation method for power system risk events based on subset simulation

Abstract

The application discloses a global sensitivity calculation method of a power system risk event based on subset simulation, establishes a representation method of a risk event in power system uncertainty quantification considering uncertainty of a random source model, applies subset simulation to decompose a rare event to reduce sampling times, and efficiently calculates global sensitivity of uncertainty of probability distribution parameters of a random source in a power system to a probability of a rare event. The scheme greatly reduces a sample size while guaranteeing accuracy of rare event probability evaluation, effectively solves the problem of low efficiency of a traditional Monte Carlo sampling algorithm in simulating a rare event, and can quickly evaluate the influence degree of uncertainty of probability distribution parameters of a random source in a power system to a probability of a rare event of power grid operation.

Description

Technical Field

[0001] This invention relates to a global sensitivity calculation method for power system risk events based on subset simulation, belonging to the field of power system uncertainty analysis technology. Background Technology

[0002] New energy power generation has reduced the proportion of traditional thermal power units, and related technology research has become a current research hotspot.

[0003] However, the randomness of load and renewable energy leads to fluctuating conditions, increasing the probability of rare risk events such as voltage overruns and line transmission power exceeding limits, posing challenges to power system operation and planning. Furthermore, the probability density functions of load and renewable energy are estimated from historical data, thus their parameters are also uncertain. To ensure the safe operation of the system, it is necessary to quantitatively assess the impact of various uncertain parameters on the probability of rare events in the power system. Global sensitivity analysis is a common tool for quantitatively assessing the impact of uncertain factors, ranking the importance of input variables. The Sobol method, a global sensitivity analysis method based on analysis of variance, is widely used due to its simple definition and significant effectiveness.

[0004] The key to calculating the global sensitivity of power system risk events is accurately assessing the probability of rare events. In existing technologies, Monte Carlo simulation (MCS) is a common sampling method; however, MCS struggles to sample rare events and capture the tail-end characteristics of the probability density function. Therefore, more efficient methods for estimating low-probability events are needed for application in global sensitivity analysis. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a global sensitivity calculation method for power system risk events based on subset simulation, applicable to power systems with renewable energy integration. This method decomposes a set of rare events into a series of larger event sets and approximates low-probability values ​​step-by-step using conditional probabilities. While ensuring the accuracy of global sensitivity for risk events, it reduces the computational burden, which is significant for improving the efficiency of uncertainty analysis in large systems.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the global sensitivity of power system risk events based on subset simulation, the method comprising the following steps:

[0007] S1. Establish a probabilistic power flow model for the power system.

[0008] S11. The formula for calculating the probabilistic power flow of the power system is as follows:

[0009] q = f(x)

[0010] Where, x={P G ,P D Q G Q D} represents the uncertainty in the system, serving as the input to the power system; f represents the steady-state power flow model; q = {P line Q line Let V,δ} represent the state variables to be determined in the system, which serve as the output of the power system;

[0011] S12. Establish a power flow model for the power system:

[0012]

[0013]

[0014] Where s represents the number of nodes; V j V i Let δ represent the voltage magnitudes at node j and node i, respectively; ji G represents the phase angle difference between nodes j and i; ji B ji P represents the conductance and susceptance of the line between nodes j and i, respectively; Dj Q Dj P represents the active power and reactive power consumed at node j, respectively; Gj Q Gj Let these represent the active power and reactive power injected at node j, respectively.

[0015] S2. Establish a characterization model for rare events in the power system that considers the uncertainties of the stochastic source model.

[0016] S21. The probability P of rare events in a power system in a model of the probability density function of a deterministic random source. f The definition of is:

[0017]

[0018] Where P(.) represents the probability of the event occurring; π represents the operating limits of the power system state variables; π(.) represents the probability density function of the random variable; X represents the complete probability space of the random variable x; ∫ X .dx represents the integral of the random variable x over the complete probability space; χ f (x) represents the 0-1 identification function corresponding to the input random variable x, defined as follows:

[0019]

[0020] S22. The probability distribution model for fluctuating load and wind speed random variables in a power system is defined as follows:

[0021] For the i-th load random variable that follows a normal distribution Its probability density function is expressed as:

[0022]

[0023] Where, ξ μi express The mean; ρ i express The ratio of the standard deviation to the mean, i.e., ρ i ξ μi express The standard deviation, in this patent, ρ i Take 0.1; n rand-load This indicates the number of random loads.

[0024] For the i-th random variable of wind speed that follows a Weibull distribution, its probability density function is expressed as:

[0025]

[0026] Where, ξ ki Indicates v i Position parameters; ξ λi Indicates v i The scale parameter; n rand-wind This indicates the number of wind farms.

[0027] The output of a wind turbine is expressed as:

[0028]

[0029]

[0030] Where, v ci The cutoff wind speed; v r Rated wind speed; v co To cut off the wind speed; P r C1 represents the rated active power output of the wind farm; C1 represents the slope.

[0031] The probability distribution parameter of uncertainty in a power system can be expressed as ξ=[ξ μ ,ξ k ,ξ λ ],in

[0032] S23. The parameters of the random source probability density function of a power system follow a uniform distribution, and its i-th uncertainty parameter ξ i The probability density function is expressed as:

[0033]

[0034] in, Let ξ represent the i-th uncertainty parameter. i The corresponding baseline value; and Let ξ represent the i-th uncertainty parameter respectively. i The lower and upper bounds of the fluctuation.

[0035] S24. Probability P of rare events in a power system with uncertain values ​​for random variable model parameters. f (ξ) is defined as:

[0036]

[0037] in, Let ξ represent the probability of a rare event under the ξ distribution; π(x|ξ) represents the conditional probability density of x with respect to ξ.

[0038] S3. Use subset simulation to decompose rare events into higher probability events to reduce the sample size and improve the efficiency of rare event probability estimation.

[0039] S31. Under the condition of ξ distribution, the event set F(ξ) of rare events is defined in the form of:

[0040]

[0041] F(ξ) represents the probability space of x under the condition of ξ distribution that satisfies The part.

[0042] Define a subset of events with increasing probability space: The corresponding event limit is satisfied

[0043] The i-th event subset i = {1, 2, ..., K} is defined as follows:

[0044] S32. Under the condition of ξ distribution, the subset simulation method expresses the probability of rare events as:

[0045]

[0046] Where ∩ represents the intersection of different events; P(F i (ξ)∣F i-1 (ξ)) represents the state in F i-1 In the event space of (ξ), F satisfies i The part of (ξ),

[0047] Set the conditional probability between any two adjacent event sets to be: P(F) i (ξ)∣F i-1 (ξ))=p0.

[0048] Estimating the probability of rare events using subset simulation. The expression is:

[0049]

[0050]

[0051] Where, N SS This represents the number of samples for each intermediate event; K represents the number of events in the event set. This represents the floor function;

[0052] S4. Calculate the first-order sensitivity of the power system model parameters based on the probability of rare events.

[0053] S41. Considering the parameter uncertainty of the probability density function of the input variables, the Sobol global sensitivity index for the probability of power system risk events is defined as:

[0054]

[0055] Where, ξ i ξ represents the i-th element in the parameter set ξ; ～i Represents ξ i The complementary subset of the remaining elements in the outer ξ; P f (ξ i ,ξ ～i ) indicates considering ξ separately i and ξ ～i The rare event probability of the parameter; D0 represents P f The total variance of (ξ); Representative targeting ξ ～i Expectations; Representative targeting ξ i The variance.

[0056] S42. The probability P of rare events under uncertain probability density function parameters estimated by subset simulation. f mean of (ξ) and variance for:

[0057]

[0058]

[0059] Where N represents the total number of samples drawn from ξ; Indicates ξi The k-th sample in; Indicates ξ ～i The kth sample in the dataset.

[0060] S43, The estimated value of the Sobol global sensitivity index under the uncertainty of the probability density function parameters mentioned in step S32 is:

[0061]

[0062] Among them, (ξ ～i )' represents ξ i Two sets of random variables that follow the same probability distribution but are independent of each other. Represents (ξ) ～i The kth sample in ').

[0063] Beneficial effects: The global sensitivity calculation method for power system risk events based on subset simulation provided by this invention establishes a characterization model of rare power system events considering the uncertainty of the random source model; it uses subset simulation to decompose rare events into higher probability events to reduce the number of samples and improve the efficiency of rare event probability estimation; and it calculates the first-order sensitivity of the uncertain power system model parameters based on the probability of rare events.

[0064] This invention significantly reduces the sample size while considering the uncertainty of the probability density function parameters of random variables, effectively solving the problem of excessive computation in traditional Monte Carlo sampling algorithms. It can quickly calculate the influence of uncertain parameters of the probability density function of power system random variables on the probability of rare events in the operation of power grid state variables. This scheme is highly adaptable, capable of assessing rare events of varying degrees and considering uncertainties of multiple parameters, providing a theoretical basis for studying the impact of uncertainty in probabilistic models on the frequency of risk events such as power exceeding limits and voltage exceeding limits in the power grid. Attached Figure Description

[0065] Figure 1 This is a flowchart of a method for calculating the global sensitivity of power system risk events based on subset simulation, according to the present invention.

[0066] Figure 2 This is a power system structure diagram in Embodiment 2 of the present invention.

[0067] Figure 3 This is a schematic diagram of the sensitivity index calculation results in Embodiment 2 of the present invention. Detailed Implementation

[0068] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 protection scope of the present invention.

[0069] Example 1: As Figure 1 As shown, a method for calculating the global sensitivity of power system risk events based on subset simulation includes the following steps:

[0070] S1. Establish a probabilistic power flow model for the power system.

[0071] S11. The formula for calculating the probabilistic power flow of the power system is as follows:

[0072] q = f(x)

[0073] Where, x={P G ,P D Q G Q D} represents the uncertainty in the system, serving as the input to the power system; f represents the steady-state power flow model; q = {P line Q line Let V,δ} represent the state variables to be determined in the system, which serve as the output of the power system;

[0074] S12. Establish a power flow model for the power system:

[0075]

[0076]

[0077] Where s represents the number of nodes; V j V i Let δ represent the voltage magnitudes at node j and node i, respectively; ji G represents the phase angle difference between nodes j and i; ji B ji P represents the conductance and susceptance of the line between nodes j and i, respectively; Dj Q Dj P represents the active power and reactive power consumed at node j, respectively; Gj Q Gj These represent the active power and reactive power injected at node j, respectively.

[0078] S2. Establish a representation model for rare events in the power system that considers the uncertainties of the stochastic source model.

[0079] S21. The probability P of rare events in a power system in a model of the probability density function of a deterministic random source. f The definition of is:

[0080]

[0081] Where P(.) represents the probability of the event occurring; π represents the operating limits of the power system state variables; π(.) represents the probability density function of the random variable; X represents the complete probability space of the random variable x; ∫ X .dx represents the integral of the random variable x over the complete probability space; χ f (x) represents the 0-1 identification function corresponding to the input random variable x, defined as follows:

[0082]

[0083] S22. The probability distribution model for fluctuating load and wind speed random variables in a power system is defined as follows:

[0084] For the i-th load random variable that follows a normal distribution Its probability density function is expressed as:

[0085]

[0086] Where, ξ μi express The mean; ρ i express The ratio of the standard deviation to the mean, i.e., ρ i ξ μi express The standard deviation, in this patent, ρ i Take 0.1; n rand-load This indicates the number of random loads.

[0087] For the i-th random variable of wind speed that follows a Weibull distribution, its probability density function is expressed as:

[0088]

[0089] Where, ξ ki Indicates v i Position parameters; ξ λi Indicates v i The scale parameter; n rand-wind This indicates the number of wind farms.

[0090] The output of a wind turbine is expressed as:

[0091]

[0092]

[0093] Where, v ci The cutoff wind speed; v r Rated wind speed; v co To cut off the wind speed; P r C1 represents the rated active power output of the wind farm; C1 represents the slope.

[0094] The probability distribution parameter of uncertainty in a power system can be expressed as ξ=[ξ μ ,ξ k ,ξ λ ],in

[0095] S23. The parameters of the random source probability density function of a power system follow a uniform distribution, and its i-th uncertainty parameter ξ i The probability density function is expressed as:

[0096]

[0097] in, Let ξ represent the i-th uncertainty parameter. i The corresponding baseline value; and Let ξ represent the i-th uncertainty parameter respectively. i The lower and upper bounds of the fluctuation.

[0098] S24. Probability P of rare events in a power system with uncertain values ​​for random variable model parameters. f (ξ) is defined as:

[0099]

[0100] in, Let ξ represent the probability of a rare event under the ξ distribution; π(x|ξ) represents the conditional probability density of x with respect to ξ.

[0101] S3. Use subset simulation to decompose rare events into higher probability events to reduce the number of samples and improve the efficiency of rare event probability estimation.

[0102] S31. Under the condition of ξ distribution, the event set F(ξ) of rare events is defined in the form of:

[0103]

[0104] F(ξ) represents the probability space of x under the condition of ξ distribution that satisfies The part.

[0105] Define a subset of events with increasing probability space: The corresponding event limit is satisfied

[0106] The i-th event subset i = {1, 2, ..., K} is defined as follows:

[0107] S32. Under the condition of ξ distribution, the subset simulation method expresses the probability of rare events as:

[0108]

[0109] Where ∩ represents the intersection of different events; P(Fi(ξ)∣Fi-1(ξ)) represents the intersection of different events in F. i-1 In the event space of (ξ), F satisfies i The part of (ξ).

[0110] Set the conditional probability between any two adjacent event sets to be: P(F) i (ξ)∣F i-1 (ξ))=p0.

[0111] Estimating the probability of rare events using subset simulation. The expression is:

[0112]

[0113]

[0114] Where, N SS This represents the number of samples for each intermediate event; K represents the number of events in the event set. This represents the floor function;

[0115] S4. Calculate the first-order sensitivity of the power system model parameters based on the probability of rare events.

[0116] S41. Considering the parameter uncertainty of the probability density function of the input variables, the Sobol global sensitivity index for the probability of power system risk events is defined as:

[0117]

[0118] Where, ξ i ξ represents the i-th element in the parameter set ξ; ～i Represents ξ i The complementary subset of the remaining elements in the outer ξ; P f (ξ i ,ξ ～i ) indicates considering ξ separately i and ξ ～i The rare event probability of the parameter; D0 represents P f The total variance of (ξ); Representative targeting ξ～i Expectations; Representative targeting ξ i The variance.

[0119] S42. The probability P of rare events under uncertain probability density function parameters estimated by subset simulation. f mean of (ξ) and variance for:

[0120]

[0121]

[0122] Where N represents the total number of samples drawn from ξ; Indicates ξ i The k-th sample in; Indicates ξ ～i The kth sample in the dataset.

[0123] S43, The estimated value of the Sobol global sensitivity index under the uncertainty of the probability density function parameters mentioned in step S32 is:

[0124]

[0125] Among them, (ξ ～i )' represents ξ i Two sets of random variables that follow the same probability distribution but are independent of each other. Represents (ξ) ～i The kth sample in ').

[0126] Example 2:

[0127] The power system structure in this embodiment is as follows: Figure 2 As shown. The system comprises a 57-node power grid and two renewable energy wind turbine generators. The uncertain distribution parameters of the location and scale parameters of the wind speed random variables at the two renewable energy wind turbine generator sites are denoted as ξ1 to ξ4, respectively; the uncertain distribution parameters of the six loads within the system are denoted as ξ5 to ξ4, respectively. 10 The correlation coefficient between the two wind speed random variables and the six load random variables remained at 0.4. Furthermore, all six loads followed a normal distribution with a standard deviation equal to 10% of the mean. The research object was the probability of rare events in active power on the line connecting node 6 and node 8. The sample size for the uncertainty parameters used in the global sensitivity analysis was 5000, and the single-layer sample size for the subset simulation algorithm used to estimate the probability of rare events was 500. The results of the global sensitivity Sobol index for rare events in the power system in this embodiment are presented. Figure 3 As shown.

[0128] Establish a characterization model for rare events in power systems that considers the uncertainties of stochastic source models;

[0129] By using subset simulation to decompose rare events into higher probability events, the number of samples can be reduced, thereby improving the efficiency of rare event probability estimation.

[0130] First-order sensitivity of power system model parameter uncertainty is calculated based on the probability of rare events.

[0131] Therefore, using set simulations to decompose rare events into higher-probability events reduces the sample size, improves the efficiency of rare event probability estimation, and efficiently solves the global sensitivity of rare events in power systems. This is of great significance for improving the efficiency of analyzing the influencing factors of rare event probabilities in large-scale systems. It provides an important guarantee for the safe, efficient, and economical operation of power systems.

[0132] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0133] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for computing global sensitivity of power system risk events based on subset simulation, characterized in that: The method includes the following steps: S1. Establish a probabilistic power flow model for the power system. S2. Establish a characterization model for rare events in the power system that considers the uncertainties of the stochastic source model. S3. Use subset simulation to decompose rare events into higher probability events to reduce the sample size and improve the efficiency of rare event probability estimation. S4. Calculate the first-order sensitivity of power system model parameter uncertainty based on the probability of rare events; Specifically, S3 uses subset simulation to decompose rare events into higher probability events to reduce the number of samples and improve the efficiency of rare event probability estimation, as detailed below: S31, in event set of rare events under distribution conditions The definition of a set is: representing in under the distribution condition the part of the probability space that satisfies the part of the probability space that satisfies Define a set of subsets of events that are increasing in the probability space: The corresponding event limits satisfy ; wherein the definition of the first subset of events is , S32, in The subset simulation method under distributed conditions expresses the probability of rare events as: in, Indicates the intersection of different events; Indicates in In the event space, satisfy Part of Set the conditional probability between any two adjacent event sets to be: , Estimating the probability of rare events using subset simulation. The expression is: in, This represents the number of samples for each intermediate event; Indicates the number of events in the event set; This represents the floor function; S4. Calculate the first-order sensitivity of the power system model parameters based on the probability of rare events, as follows: S41. Considering the parameter uncertainty of the probability density function of the input variables, the Sobol global sensitivity index for the probability of power system risk events is defined as: in, Represents parameter set The first in One element; Representative except outside The complementary subset of the remaining elements; Indicates consideration separately and The probability of rare events for the parameter; express The total variance; Representatives targeting Expectations; Representatives targeting The conditional variance of S42. Probability of rare events under uncertain probability density function parameters estimated by subset simulation mean and variance for: in, Indicates in The total number of samples drawn from the sample; express The first in One sample; express The first in One sample, S43, The estimated value of the Sobol global sensitivity index under the uncertainty of the probability density function parameters mentioned in step S32 is: in, express Two sets of independent random variables with the same probability distribution. Indicates from The first sampled from a random variable A sample is used to estimate the conditional variance in step S41. The value of transforms the conditional variance into two sets of rare probabilities. and The mean of the product; step S43 calculates a sensitivity index for the probability of rare events, which serves as the basis for ranking the importance of the distribution parameters of the probability density function of random variables on the probability of rare events.

2. The method for calculating the global sensitivity of power system risk events based on subset simulation according to claim 1, characterized in that: S1. Establish a probabilistic power flow model for the power system, as follows: S11. The formula for calculating the probabilistic power flow of the power system is as follows: in, It represents the uncertainty in the system and serves as the input to the power system; A model representing the steady-state power flow of electricity; , representing the state variable to be determined in the system, which serves as the output of the power system; S12. Establish a power flow model for the power system: in, Indicates the number of nodes; , Representing nodes respectively ,node The magnitude of the voltage at that point; Represents a node and The phase angle difference between them; , Representing nodes respectively and The conductance and susceptance of the lines between them; , Representing nodes respectively The active and reactive power consumed at the point; , Representing nodes respectively The active and reactive power injected at the point.

3. The method for calculating the global sensitivity of power system risk events based on subset simulation according to claim 1, characterized in that: S2. Establish a representation model for rare events in the power system that considers the uncertainties of the stochastic source model, as follows: S21. Probability of rare events in a power system in a model of the probability density function of a deterministic random source. The definition of is: in, Indicates the probability of an event occurring; Indicates the operating limits of power system state variables; The probability density function representing a random variable; Represents random variables The complete probability space; Represents the relationship between random variables Integral over the complete probability space; Indicates input random variables The corresponding 0-1 recognition function is defined as follows: S22. The probability distribution model for fluctuating load and wind speed random variables in a power system is defined as follows: For the A load random variable that follows a normal distribution Its probability density function is expressed as: in, express The mean; express The ratio of the standard deviation to the mean, i.e. express standard deviation For the Let there be a random variable of wind speed that follows a Weibull distribution, and its probability density function be expressed as: in, express Position parameters; express Scale parameters; Indicates the number of wind farms. The output of a wind turbine is expressed as: in, Cutoff wind speed; Rated wind speed; To cut off the wind speed; This refers to the rated active power output of the wind farm. Indicates the slope. The probability distribution parameters of uncertainty in a power system can be expressed as follows: ,in , , , S23. The parameters of the random source probability density function of a power system follow a uniform distribution, and its i-th... Uncertainty parameters The probability density function is expressed as: in, Indicates the first Uncertainty parameters The corresponding baseline value; and They represent the first Uncertainty parameters The lower and upper bounds of the fluctuation. S24. Probability of rare events in power systems with uncertain values ​​for random variable model parameters. Defined as: in, Indicates in Probability of rare events under given distribution conditions; express for The conditional probability density.

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