Electrothermal coupling probabilistic load flow calculation method considering time correlation characteristics of input variables

Abstract

An electrothermal coupling probabilistic load flow calculation method considering time correlation characteristics of an input variable comprises the following steps: introducing an adaptive window width reflection kernel density estimation method to fit wind speed data, and establishing an uncertainty model of the input variable; a Sobol random sequence obeying [0, 1] uniform distribution is generated, a random number sequence considering time correlation is generated by using a position sorting method according to input actual measurement data, and finally a wind speed sequence sample is obtained through a cubic spline interpolation method. Inputting structural parameters of a power system, introducing a heat balance equation, and establishing an electrothermal coupling probabilistic load flow calculation model by being combined with a probabilistic load flow calculation model; and initializing the model, inputting a wind temperature sequence of each scene, and carrying out electrothermal coupling probabilistic load flow calculation by utilizing a Monte Carlo simulation method distribution based on a Sobol sequence. Uncertainty modeling is carried out according to a model output result, the result is evaluated and analyzed, and a conclusion is obtained. The method is of great significance in analyzing the operation condition of the power system and further guaranteeing safe and stable operation of the power system.

Description

Technical Field

[0001] The present invention belongs to the field of power system uncertainty modeling and probabilistic power flow calculation, and in particular relates to an electric-thermal coupling probabilistic power flow calculation method taking into account the time-related characteristics of input variables. Background Art

[0002] The capacity of new clean energy access systems such as wind power and solar energy continues to grow rapidly, and the power system has gradually evolved into a "double-high" power system with a "high proportion of new energy" connected to the grid and a "high proportion of power electronic equipment" fed in. This has led to a significant increase in uncertainties in the operation planning of new power systems, posing challenges to the economy, safety and reliability requirements of system operation and planning. The probabilistic power flow method can effectively consider the impact of various random uncertainty factors on the power system power flow characteristics.

[0003] The document with application publication number CN117977596A discloses a method and system for calculating the probability flow of a regional power grid connected to distributed photovoltaics. The specific steps include: using the maximum likelihood estimation method to solve the pre-built adaptive multidimensional Gaussian mixture model to obtain the probability density function of the distributed photovoltaic output data with correlated random variables. The probability density function of the distributed photovoltaic output data is transformed into a state using a third-order polynomial normal transformation to obtain the probability density function of the distributed photovoltaic output data with independent normal random variables. Based on the probability density function of the distributed photovoltaic output data with independent normal random variables, the node voltage distribution and line flow distribution of the regional power grid connected to distributed photovoltaics are obtained as the flow calculation result; the document with application publication number CN104751006B discloses a method for calculating the probability flow taking into account the correlation of variables. The specific steps include: obtaining conventional flow calculation data and deterministic flow calculation. Obtaining a calculation model for the influence of changes in power injection of PV nodes and PQ nodes on node voltage. Using a normally distributed polynomial to represent a non-normally distributed random variable. Using Cholesky decomposition to convert correlated random variables into uncorrelated random variables. Probabilistic power flow calculation is performed on the variables. This method improves the calculation speed while ensuring the calculation accuracy. It can be applied to complex power grid system analysis and safety assessment after large-scale intermittent energy is connected to the grid, and can effectively improve the new energy acceptance capacity of the power system. The document with application publication number CN118551538A discloses a probabilistic power flow calculation method based on data-driven adaptive chaotic polynomial expansion. First, historical data samples of active power of photovoltaic power stations are collected. The expansion order is set, all monomials corresponding to the input variables that meet the expansion order are constructed, and the monomial vectors are obtained by merging according to the specified monomial order. Whitening transformation is constructed based on the monomial vector to obtain an orthogonal polynomial vector. An adaptive polynomial approximation model of the mapping relationship between power flow output variables and active power historical data samples in the power system is constructed. The adaptive polynomial approximation model is used to evaluate the active power historical data samples of photovoltaic power stations, and the samples and probability density functions of power flow output variables in the power system are obtained. This method is completely data-driven, can adapt to input variables with arbitrary distribution and arbitrary correlation, has extremely high universality, and greatly improves the calculation efficiency while ensuring high probability power flow calculation accuracy.

[0004] Traditional probabilistic power flow calculation methods usually ignore the time-dependent characteristics of these environmental factors, resulting in low accuracy and reliability of the evaluation results. Therefore, it is particularly important to develop an electrothermal coupled probabilistic power flow calculation method that can consider the time-dependent characteristics of the input variables. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an electrothermal coupling probabilistic power flow calculation method taking into account the time-related characteristics of input variables, so as to solve the problem that the current literature does not consider the influence of environmental factors on line parameters in the probabilistic power flow calculation of the power system, resulting in poor accuracy of the model output power flow calculation results, etc., and consider the time correlation of the input variables, introduce the thermal balance equation into the field of probabilistic power flow calculation with line temperature and impedance parameters as the link, and use the Monte Carlo simulation method based on low-deviation Sobol sequence optimization to perform probabilistic power flow calculation, and propose an electrothermal coupling probabilistic power flow calculation model taking into account the time-related characteristics.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: A method for calculating the electrothermal coupling probabilistic power flow considering the time-dependent characteristics of the input variables, the steps are: Step 1: Input the measured wind speed and temperature series data, process the data, introduce the adaptive window width reflection kernel density estimation method to fit the wind speed data, and establish the uncertainty model of the input variables; Step 2: Generate a Sobol random sequence that obeys the uniform distribution of [0,1], generate a random number sequence that takes into account time correlation based on the input measured data using the position sorting method, and finally obtain the wind speed sequence sample through the cubic spline interpolation method; Step 3: Input the power system structural parameters, introduce the heat balance equation, and establish the electric-thermal coupling probabilistic power flow calculation model by combining it with the probabilistic power flow calculation model; Step 4: Initialize the electric-thermal coupling probabilistic power flow calculation model, input the wind temperature sequence of each scene, and use the Monte Carlo simulation method based on the Sobol sequence to perform the electric-thermal coupling probabilistic power flow calculation; Step 5: Conduct uncertainty modeling based on the model output, evaluate and analyze the results, and draw conclusions.

[0007] Preferably, in step 1, an adaptive window width reflection kernel density estimation method is introduced to perform uncertainty modeling on the input wind temperature sequence, which includes the following steps: Step 1-1: The type of kernel function has little effect on the accuracy of the fitting result. A Gaussian function with high smoothness and good differentiability is selected as the kernel function, that is: (1); In the formula, represents the Gaussian kernel input random variable.

[0008] Step 1-2: Use reflection kernel density estimation to establish the wind speed probability density function. Reflect the original data with the left and right boundaries of the interval as the symmetry axis to obtain the reflected data. Perform kernel density estimation based on the original data and reflected data, and input the random variable The original sample on the interval [0,1] is , the reflection sample is , the kernel density estimation function of the data is obtained as: (2); In the formula, represents the kernel function, is the window width; is the number of samples; For the samples; By improving the fitting deviation of the conventional kernel density estimation at the boundary points, the non-parametric kernel density estimation model of wind speed based on the data reflection principle is obtained as follows: (3); In the formula, is the upper bound of wind speed fluctuation; is the wind speed random variable; ; ; For the wind speed samples; Step 1-3: Adaptively select the appropriate window width by using an improved interpolation method that does not require prior assumptions , the wind speed probability density function of the adaptive window width reflection kernel density estimation is obtained as: (4).

[0009] Preferably, in step 2, a Sobol sequence with more uniform distribution is introduced to generate a random sequence sample that obeys a [0,1] uniform distribution, a random number sequence taking into account time correlation is generated according to the input measured data using a position sorting method, and finally a random wind speed sequence is generated according to the established wind speed probability density distribution model using a cubic spline interpolation method, which includes the following steps: Step 2-1: By comparing and analyzing the pseudo-random sequence samples generated by the conventional Monte Carlo method and the Sobol sequence samples, it is found that the Sobol sequence has better uniformity than the pseudo-random number, and the Sobol sequence is selected to generate the random sequence; Step 2-2: By inputting the numerical order of the wind speed in the original measured wind speed sequence, the Sobol sequence random numbers are sorted using the position sorting method to obtain a time-related random number sequence; Step 2-3: Based on the probability distribution function established using the measured wind speed sequence, a cubic spline interpolation method is used to generate wind speed sequence samples corresponding to a random number sequence with time correlation.

[0010] Preferably, in step 2-1, a low-deviation sequence Sobol sequence is used, and each primitive polynomial can generate a one-dimensional Sobol sequence. Different primitive polynomials can generate the required dimensional Sobol sequence, using low-order primitive polynomials to generate Sobol sequences, generated according to the input wind speed sequence dimensional Sobol sequence.

[0011] Preferably, in step 2-2, a position sorting method is used to consider time correlation; first generate dimensional Sobol sequence random numbers , input the measured wind speed sequence ,remember For variables In vector To sort the positions from small to large, the steps are as follows: (1) and Arrange the elements in each column from large to small to obtain their corresponding position vectors and ; (2) First take out The first column of data in , and find the corresponding ; (3) From Location Replace with , and continue to make the same replacement for other data in the column; (4) According to steps (1) to (3), the data of each column of the Sobol sequence is sorted and processed, and finally a set of Sobol random number sequences that retain the time correlation of the measured wind speed is obtained. .

[0012] Preferably, in step 2-3, the wind speed sample corresponding to the Sobol random number sequence is obtained by using the cubic spline interpolation method. The cubic spline interpolation method is a curve fitting method based on the cubic spline function, and its basic definition is: Let in the interval Given a certain node partition (5); In the formula, represents the interval boundary, Represents an interval partitioning node.

[0013] If there is a positive integer make Piecewise function on The following conditions are met: 1) In the interval Memory Derivatives; 2) In each interval All are polynomials of order no greater than three; Then it is called So is a cubic spline function of a node set. If the function The node function value is: (6); And the cubic spline function of the node set Satisfy the interpolation conditions: (7); Then this cubic spline function This is the cubic spline interpolation function.

[0014] In the formula, is the cubic spline function variable, is the corresponding cubic spline function value.

[0015] Preferably, in step 3, the influence of environmental factors on the transmission line parameters is taken into account by introducing a heat balance equation, and a probabilistic power flow calculation model of electric-thermal coupling is established by combining the line impedance and temperature with the probabilistic power flow calculation equation, and the steps are as follows: Step 3-1: Collect data on environmental factors such as wind speed and temperature around the line and introduce the heat balance equation; (8); In the formula, The heat generated by the current flowing through the conductor of the wire; The heat generated by sunlight shining on the transmission lines; The heat dissipation is caused by air convection; Radiate heat for the circuit; Step 3-2: Add the probability power flow calculation equation and combine them to get the complete model; (9); In the formula, Node The active power and reactive power of Node The voltage amplitude, For Node The voltage phase angle With Node The voltage phase angle difference, They are the node conductance matrix and the node susceptance matrix, respectively, written in matrix form: (10); In the formula, Represents the injected active power of all nodes except the balancing node and reactive power , The state variables representing the voltage magnitude and phase angle of all nodes except the equilibrium node, Represents the output quantity, including the active power and reactive power flowing in each branch; Represent the relevant equations of node voltage and branch power respectively.

[0016] Preferably, in step 4, the wind speed and temperature are used as input variables, and the probabilistic power flow calculation is performed using the low-deviation sequence improved Monte Carlo simulation method.

[0017] Preferably, in step 5, a kernel density estimation method is used to establish a probability density function for the model outputs such as node voltage and branch active power, and an analysis and evaluation is performed to verify the effectiveness and accuracy of the model.

[0018] An electrothermal coupling probabilistic power flow calculation model considering the time-related characteristics of input variables adopts the electrothermal coupling probabilistic power flow calculation method considering the time-related characteristics of input variables.

[0019] The present invention can achieve the following beneficial effects: 1. The adaptive window width reflection kernel density estimation method is introduced to fit the wind temperature data and accurately establish the uncertainty model of the input variables.

[0020] 2. Use low-deviation Sobol sequence instead of pseudo-random sequence to generate more uniform random data, and use position sorting method to give time correlation to the random sequence according to the input measured wind temperature data to obtain a time-correlated wind temperature random sequence.

[0021] 3. Taking the temperature and impedance parameters of the transmission line as the link, the thermal balance equation is introduced to consider the impact of environmental factors around the line on the line impedance, and then the line parameters are corrected to reduce the model error.

[0022] 4. Probabilistic power flow calculation is performed based on the modified impedance parameters and wind temperature sequence, and the kernel density estimation method is used to describe the model output to obtain probability density functions of variables such as branch active power and node voltage that are more in line with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will be further described below in conjunction with the accompanying drawings and embodiments: Figure 1 is a flow chart of the method of the present invention; Figure 2 Input the measured wind temperature time series curve; Figure 3 This is a comparison diagram of the data point distribution between the two-dimensional Sobol sequence and the pseudo-random sequence; Figure 4It is a comparison diagram of the probability density function of the node voltage amplitude before and after considering thermal balance; Figure 5 It is a comparison chart of the probability density function of the node voltage amplitude under the random sequence of wind temperature before and after considering the time correlation and the measured wind temperature data. DETAILED DESCRIPTION

[0024] The preferred solution is Figures 1 to 5 As shown in Figure 1, a method for calculating the electrothermal coupling probabilistic power flow considering the time-dependent characteristics of the input variables is as follows: Step 1: Input the measured wind speed and temperature series data, preprocess the data, introduce the adaptive window width reflection kernel density estimation method to fit the wind temperature data, and establish the probability density function of the input variables.

[0025] Step 2: Generate a Sobol random sequence that obeys the uniform distribution of [0,1]. Generate a random number sequence that takes time correlation into account using the position sorting method based on the input measured data. Finally, obtain the wind speed sequence sample through the cubic spline interpolation method.

[0026] Step 3: Input the power system structural parameters, introduce the heat balance equation, and establish the electric-thermal coupling probabilistic power flow calculation model by combining it with the probabilistic power flow calculation model.

[0027] Step 4: Initialize the model, input the wind temperature sequence of each scene, and use the Monte Carlo simulation method based on the Sobol sequence to perform the electric-thermal coupling probabilistic power flow calculation.

[0028] Step 5: Conduct uncertainty modeling based on the model output, evaluate and analyze the results, and draw conclusions.

[0029] In step 1: input the measured wind speed and temperature series data, preprocess the data, introduce the adaptive window width reflection kernel density estimation method to fit the wind temperature data, and establish the probability density function of the input variables. Specifically, the following steps are included: Step 1-1: The type of kernel function has little effect on the accuracy of the fitting result, so a Gaussian function with high smoothness and good differentiability is directly selected as the kernel function: (1); In the formula, represents the Gaussian kernel input random variable.

[0030] Step 1-2: Use reflection kernel density estimation to establish the wind speed probability density function. Reflect the original data with the left and right boundaries of the interval as the symmetry axis to obtain the reflected data. Perform kernel density estimation based on the original data and reflected data, and input the random variable The original sample on the interval [0,1] is , the reflection sample is , the kernel density estimation function of the data is obtained as: (2); In the formula, represents the kernel function, is the window width; is the number of samples; For the samples.

[0031] By improving the fitting deviation of the conventional kernel density estimation at the boundary points, the non-parametric kernel density estimation model of wind speed based on the data reflection principle is obtained as follows: (3); Where: is the upper bound of wind speed fluctuation; is the wind speed random variable; ; ; For the wind speed samples.

[0032] Step 1-3: Adaptively select the appropriate window width by using the advanced plug-in (PI) method without prior assumptions , the wind speed probability density function of the adaptive window width reflection kernel density estimation is obtained as: (4); In step 2: a more uniformly distributed Sobol sequence is introduced to generate a random sequence sample that obeys a uniform distribution of [0,1]. A random number sequence that takes into account time correlation is generated based on the input measured data using the position sorting method. Finally, a random sequence of wind speed is generated based on the established wind speed probability density distribution model using the cubic spline interpolation method. Specifically, the following steps are included: Step 2-1: By comparing and analyzing the pseudo-random sequence samples and Sobol sequence samples generated by the conventional Monte Carlo method, the specific Figure 3 The Sobol sequence obtained in the above equation has better uniformity than pseudo-random numbers, so the Sobol sequence is selected to generate random sequences. Using the low-deviation sequence Sobol sequence, each primitive polynomial can generate a one-dimensional Sobol sequence. In practical problems, we only need to select Different primitive polynomials can generate the required dimensional Sobol sequence, but usually only low-order primitive polynomials are used to generate Sobol sequences, because as the number of primitive polynomials increases, the dimension of the Sobol sequence increases, and its advantage in uniformity will weaken. In this paper, only the input wind speed sequence is needed to generate dimensional Sobol sequence.

[0033] Step 2-2: By inputting the numerical order of the wind speed in the original measured wind speed sequence, the Sobol sequence random numbers are sorted using the position sorting method to obtain a time-related random number sequence. The position sorting method is used to consider time correlation. First generate dimensional Sobol sequence random numbers , input the measured wind speed sequence ,remember For variables In vector The rankings in ascending order are as follows: (1) and Arrange the elements in each column from large to small to obtain their corresponding position vectors and .

[0034] (2) First take out The first column of data in , and find the corresponding .

[0035] (3) From Location Replace with , and continue to make the same replacement for other data in the column.

[0036] (4) According to steps (1) to (3), the data of each column of the Sobol sequence is sorted and processed, and finally a set of Sobol random number sequences that retain the time correlation of the measured wind speed is obtained. .

[0037] Step 2-3: Based on the probability distribution function established using the measured wind speed sequence, use the cubic spline interpolation method to generate wind speed sequence samples corresponding to the random number sequence with time correlation. The cubic spline interpolation method is a curve fitting method based on the cubic spline function, and its basic definition is: Let in the interval Given a certain node partition (5); In the formula, represents the interval boundary, Represents an interval partitioning node.

[0038] If there is a positive integer make Piecewise function on The following conditions are met: 1) In the interval Memory Derivatives; 2) In each interval All are polynomials of order no greater than three; Then it is called So is a cubic spline function of a node set. If the function The node function value is: (6); And the cubic spline function of the node set Satisfy interpolation conditions (7); Then this cubic spline function This is the cubic spline interpolation function.

[0039] In the formula, is the cubic spline function variable, is the corresponding cubic spline function value.

[0040] In step 3: the influence of environmental factors on transmission line parameters is taken into account by introducing the heat balance equation, and the electric-thermal coupled probabilistic power flow calculation model is established by combining the line impedance and temperature with the probabilistic power flow calculation equation. The specific steps are as follows: Step 3-1: Collect data on environmental factors such as wind speed and temperature around the line and introduce the heat balance equation.

[0041] (8); In the formula, The heat generated by the current flowing through the conductor of the wire; The heat generated by sunlight shining on the transmission lines; The heat dissipation is caused by air convection; The heat dissipation of the wire itself mainly comes from the power loss caused by the current flowing through the line, which is expressed as: (9); In the formula, the heat generated by the current is The current flowing through the line I and the resistance of the line R The impedance of the circuit is related to the temperature of the circuit. The specific relationship is shown in the formula: (10); In the formula, is the line skin effect coefficient; At the reference temperature AC reference resistance when ; The reference temperature of the conductor is The corresponding resistance temperature coefficient is usually taken as .

[0042] The heat absorption from sunlight is the only factor that is not affected by the line temperature, and its power expression is: (11); In the formula, is the conductor heat absorption coefficient, is the effective radiation intensity of sunlight, ; is the wire diameter, .

[0043] Step 3-2: Add the probabilistic power flow calculation equation and combine them to obtain the complete model.

[0044] (12); In the formula, Node The active power and reactive power of Node The voltage amplitude, For Node The voltage phase angle With Node The voltage phase angle difference, They are the node conductance matrix and the node susceptance matrix, respectively, written in matrix form: (13); In the formula, Represents the injected active power of all nodes except the balancing node and reactive power , The state variables representing the voltage magnitude and phase angle of all nodes except the equilibrium node, Represents the output quantity, including the active power and reactive power flowing through each branch. Represent the relevant equations of node voltage and branch power respectively.

[0045] In step 4, wind speed and temperature are used as input variables and the probabilistic power flow calculation is performed using the low-bias sequence improved Monte Carlo simulation method.

[0046] In step 5, the kernel density estimation method is used to establish the probability density function of the model outputs such as node voltage and branch active power, and the analysis and evaluation are carried out to verify the effectiveness and accuracy of the model.

[0047] Example: To verify the effectiveness and accuracy of the present invention, the present invention selects the IEEE 30-node test system to perform simulation on the MATLAB platform based on the Matpower toolkit. The input wind temperature data used in the experiment comes from the actual measurement data of the Measurement and Instrumentation Data Center (MIDC) of the National Renewable Energy Laboratory (NREL) of the United States at Elizabeth City State University. The data duration is 1 year (January 2010 to December 2010), the time interval is 1 hour, and the total number of data points is 8760. Figure 2 shown.

[0048] Figure 2 The data are further divided into winter scenarios (January to April) and summer scenarios (June to September) to further evaluate and analyze the model.

[0049] from Figure 3 It can be seen that the Sobol sequence is more uniform than the conventional pseudo-random sequence and can more accurately reflect the distribution information of the input wind temperature data.

[0050] from Figure 4 It can be seen that after the impedance parameters of the transmission line are corrected by considering environmental factors, the power flow calculation results change, and the changes show obvious differences in different seasonal scenarios. Specifically, in the winter period, the voltage amplitude probability density curve of node 19 shifts to the right, the voltage amplitude increases, and the active power loss probability density curve of branch 12-16 shifts to the left, and the active power loss of the branch is significantly reduced by 3.58%, which is mainly due to the small line impedance in winter. In the summer period, the change trend is just the opposite of that in winter, the node voltage amplitude decreases, and the active power loss of the branch increases by 5.19%.

[0051] Depend on Figure 5 It can be seen that the probability flow calculation results obtained after considering the time series correlation between wind speed and temperature are closer to the results under the actual wind temperature series data than the probability flow results without considering the time series correlation between wind and temperature. The effectiveness of the model is verified by evaluating the flow results before and after considering the correlation using the mean absolute error MAE (Mean Absolute Error) and the root mean square error RMSE (Root MeanSquare Error). Figure 5 After considering the time series correlation of input variables, the MAE and RMSE of the probability density curve of the voltage amplitude of node 19 are reduced by 80.7% and 72.1% respectively, and the active power loss of branches 12-16 is reduced by 70.1% and 71.7% respectively. From the simulation test results, it can be concluded that the electrothermal coupling probabilistic power flow calculation model after considering thermal balance can effectively take into account the impact of environmental factors on transmission line parameters, correct the power flow results, and further accurately describe the operation of the power system through probabilistic power flow while considering the time series correlation of input variables such as wind speed.

[0052] The electric-thermal coupled probabilistic power flow ETC-PPF calculation model proposed in the present invention, which takes into account the time-related characteristics of the input variables, is of great significance for accurately reflecting the operation of the power system and ensuring the safe, economical and stable operation of the power system.

[0053] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of the input variables, characterized in that The following steps are involved: Step 1: Input the measured wind speed and temperature series data, process the data, introduce the adaptive window width reflection kernel density estimation method to fit the wind speed data, and establish the uncertainty model of the input variables; Step 2: Generate a Sobol random sequence that obeys the uniform distribution of [0,1], generate a random number sequence that takes into account time correlation based on the input measured data using the position sorting method, and finally obtain the wind speed sequence sample through the cubic spline interpolation method; Step 3: Input the power system structural parameters, introduce the heat balance equation, and establish the electric-thermal coupling probabilistic power flow calculation model by combining it with the probabilistic power flow calculation model; Step 4: Initialize the electric-thermal coupling probabilistic power flow calculation model, input the wind temperature sequence of each scene, and use the Monte Carlo simulation method based on the Sobol sequence to perform the electric-thermal coupling probabilistic power flow calculation; Step 5: Conduct uncertainty modeling based on the model output, evaluate and analyze the results, and draw conclusions.

2. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 1 is characterized in that: In step 1, the adaptive window width reflection kernel density estimation method is introduced to model the uncertainty of the input wind temperature series, which includes the following steps: Step 1-1: The type of kernel function has little effect on the accuracy of the fitting result. A Gaussian function with high smoothness and good differentiability is selected as the kernel function, that is: （1）； In the formula, represents the Gaussian kernel function input random variable; Step 1-2: Use reflection kernel density estimation to establish the wind speed probability density function. Reflect the original data with the left and right boundaries of the interval as the symmetry axis to obtain the reflected data. Perform kernel density estimation based on the original data and reflected data, and input the random variable The original sample on the interval [0,1] is , the reflection sample is , the kernel density estimation function of the data is: （2）； In the formula, represents the kernel function, is the window width; is the number of samples; For the samples; By improving the fitting deviation of the conventional kernel density estimation at the boundary points, the non-parametric kernel density estimation model of wind speed based on the data reflection principle is obtained as follows: （3）； In the formula, is the upper bound of wind speed fluctuation; is the wind speed random variable; ; ; For the wind speed samples; Step 1-3: Adaptively select the appropriate window width by using an improved interpolation method that does not require prior assumptions , the wind speed probability density function of the adaptive window width reflection kernel density estimation is obtained as: （4）。 3. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 1 is characterized in that: In step 2, the Sobol sequence with more uniform distribution is introduced to generate random sequence samples that obey the [0,1] uniform distribution. The position sorting method is used to generate a random number sequence that takes into account time correlation based on the input measured data. Finally, the cubic spline interpolation method is used to generate a wind speed random sequence based on the established wind speed probability density distribution model, which includes the following steps: Step 2-1: By comparing and analyzing the pseudo-random sequence samples generated by the conventional Monte Carlo method and the Sobol sequence samples, it is found that the Sobol sequence has better uniformity than the pseudo-random number, and the Sobol sequence is selected to generate the random sequence; Step 2-2: By inputting the numerical order of the wind speed in the original measured wind speed sequence, the Sobol sequence random numbers are sorted using the position sorting method to obtain a time-related random number sequence; Step 2-3: Based on the probability distribution function established using the measured wind speed sequence, a cubic spline interpolation method is used to generate wind speed sequence samples corresponding to a random number sequence with time correlation.

4. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 3 is characterized in that: In step 2-1, a low-deviation sequence Sobol sequence is used. Each primitive polynomial can generate a one-dimensional Sobol sequence. Select Different primitive polynomials can generate the required dimensional Sobol sequence, using low-order primitive polynomials to generate Sobol sequences, generated according to the input wind speed sequence dimensional Sobol sequence.

5. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 3 is characterized in that: In step 2-2, the position sorting method is used to consider the time correlation; first generate dimensional Sobol sequence random numbers , input the measured wind speed sequence ,remember For variables In vector To sort the positions from small to large, the steps are as follows: (1) and Arrange the elements in each column from large to small to obtain their corresponding position vectors and ; (2) First take out The first column of data in , and find the corresponding ; (3) From Location Replace with , and continue to make the same replacement for other data in the column; (4) Sort the data in each column of the Sobol sequence according to steps (1) to (3), and finally obtain a set of Sobol random number sequences that retain the time correlation of the measured wind speed. .

6. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 3 is characterized in that: In step 2-3, the wind speed sample corresponding to the Sobol random number sequence is obtained by using the cubic spline interpolation method. The cubic spline interpolation method is a curve fitting method based on the cubic spline function, and its basic definition is: Let in the interval Given a certain node partition （5）； In the formula, represents the interval boundary, Represents interval partitioning node; If there is a positive integer make Piecewise function on The following conditions are met: 1) In the interval Memory Derivatives; 2) In each interval All are polynomials of order no greater than three; Then it is called So is a cubic spline function of a node set. If the function The node function value is: （6）； And the cubic spline function of the node set Satisfy the interpolation conditions: （7）； Then this cubic spline function That is the cubic spline interpolation function; In the formula, is the cubic spline function variable, is the corresponding cubic spline function value.

7. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 1 is characterized in that: In step 3, the influence of environmental factors on the transmission line parameters is taken into account by introducing the heat balance equation. The line impedance and temperature are used as the link to establish the electric-thermal coupled probabilistic power flow calculation model in conjunction with the probabilistic power flow calculation equation. The steps are as follows: Step 3-1: Collect data on environmental factors such as wind speed and temperature around the line and introduce the heat balance equation; （8）； In the formula, The heat generated by the current flowing through the conductor of the wire; The heat generated by sunlight shining on the transmission lines; The heat dissipation is caused by air convection; Radiate heat for the circuit; Step 3-2: Add the probability power flow calculation equation and combine them to get the complete model; （9）； In the formula, Node The active power and reactive power of Node The voltage amplitude, For Node The voltage phase angle With Node The voltage phase angle difference, They are the node conductance matrix and the node susceptance matrix, respectively, written in matrix form: （10）； In the formula, Represents the injected active power of all nodes except the balancing node and reactive power , The state variables representing the voltage magnitude and phase angle of all nodes except the equilibrium node, Represents the output quantity, including the active power and reactive power flowing in each branch; Represent the relevant equations of node voltage and branch power respectively.

8. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 1, characterized in that: In step 4, wind speed and temperature are used as input variables and the probabilistic power flow calculation is performed using the low-bias sequence improved Monte Carlo simulation method.

9. The method for calculating the electric-thermal coupling probabilistic power flow considering the time-dependent characteristics of input variables according to claim 1, characterized in that: In step 5, the kernel density estimation method is used to establish the probability density function of the model outputs such as node voltage and branch active power, and the analysis and evaluation are carried out to verify the effectiveness and accuracy of the model.

10. An electric-thermal coupling probabilistic power flow calculation model considering the time-dependent characteristics of input variables, characterized by: An electrothermal coupling probabilistic power flow calculation method taking into account the time-dependent characteristics of input variables according to any one of claims 1 to 9 is adopted.

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