Electric power system nonparametric probabilistic load flow calculation method considering complex uncertainty

Abstract

The invention discloses a non-parametric probabilistic load flow calculation method considering complex uncertainty for a power system. The method comprises the following steps: firstly, constructing source-load nonparametric probability distribution based on a multivariate Gaussian mixture model; then, constructing an alternating current power flow model under a polar coordinate system in the power system, and performing linear expansion on the alternating current power flow model under the polar coordinate system in the power system at a mean point of source-load non-parametric probability distribution by adopting a first-order Taylor series approximation method to obtain a system operation simplified model based on alternating current power flow linearization of the power system; and finally, according to the linear transformation property of the Gaussian distribution, obtaining the probability distribution of the power flow distribution of the power system under each Gaussian component, and in combination with the total probability law, carrying out weighted summation on the probability distribution under each Gaussian component according to the weight to obtain the non-parametric probabilistic power flow probability distribution of the power system. The method provided by the invention has stronger generalization ability and accuracy, and has important reference significance for operation uncertainty quantification of the power system under complex uncertainty.

Description

Technical Field

[0001] The present invention belongs to the field of power system analysis, and particularly relates to a non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties. Background Art

[0002] Compared with primary energy sources, renewable energy sources such as wind power and photovoltaic power have the advantages of environmental friendliness and sustainability. However, due to the chaotic nature of the atmospheric system, the output of new energy sources such as wind power has characteristics of high uncertainty and strong volatility, and the power flow distribution of the power system shows high probability characteristics. Therefore, it is of great significance to carry out research on probabilistic power flow considering complex uncertainties. The input probability distributions of traditional probabilistic power flow calculation methods need to be parameterized, resulting in large errors. There is an urgent need to propose a non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties. Summary of the Invention

[0003] The purpose of the present invention is to provide a non-parametric probabilistic power flow calculation method for power systems that quantifies the uncertainty of power flow distribution in new energy power systems. A non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties according to the present invention takes into account the correlation and non-parametric distribution characteristics of complex random variables and has high generalization ability.

[0004] To achieve the above object, the technical solution adopted by the present invention is:

[0005] A non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties, which is used to analyze the steady-state operation of power systems under source-load randomness. The non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties is as follows:

[0006] Construct a source-load non-parametric probability distribution based on a multivariate Gaussian mixture model: Obtain source-load uncertainty data based on probability prediction, sample the obtained source-load uncertainty data, screen and remove outlier data values, and perform parameter estimation of the multivariate Gaussian mixture model on the screened sampled data to obtain a source-load non-parametric probability distribution;

[0007] Construct a simplified system operation model based on the linearization of the AC power flow of the power system: Construct an AC power flow model in the polar coordinate system of the power system, and perform linear expansion on the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution by using the first-order Taylor series approximation method to obtain a simplified system operation model based on the linearization of the AC power flow of the power system;

[0008] Perform non-parametric probability mapping on the power flow distribution of the power system: Based on the simplified system operation model of the AC power flow linearization of the power system, combined with the linear transformation method of the Gaussian distribution, obtain the probability distribution of the power flow distribution of the power system under each Gaussian component; According to the law of total probability, perform weighted summation of the probability distributions of the power flow distribution of the power system under each Gaussian component by weight to obtain the non-parametric probability power flow probability distribution of the power system.

[0009] In the above technical solution, further, the multivariate Gaussian mixture model can fit probability distributions of any distribution form and has non-parametric probability characteristics. The specific expression of the probability density function of the multivariate Gaussian mixture model is:

[0010]

[0011] where x represents the random vector composed of the filtered new energy power and load; f GMM (x|Θ) represents the value of the probability density function of the random variable described by the multivariate Gaussian mixture model; f N (x; μ i , Σ i ) represents the i-th Gaussian component in the multivariate Gaussian mixture model; ω i , μ i and Σ i represent the weight, mean vector and covariance matrix of the i-th Gaussian component respectively; n is the number of Gaussian components in the multivariate Gaussian mixture model; Θ is the set of parameters to be solved, and its expression is:

[0012]

[0013] where the value of the set of parameters to be solved Θ is usually calculated using the expectation maximization algorithm, which can be specifically divided into two steps:

[0014] E-step (E-step): Calculate the probability that the data comes from each Gaussian component based on the current parameter values. Let the probability that the sample x k in x comes from the i-th Gaussian component be γ ki , and its calculation formula is:

[0015]

[0016] where f N (x k ; μ i , Σ i ) represents the value of the probability density function of the sample x k under the i-th Gaussian component; f N (x k ; μ j , Σ j ) represents the value of the probability density function of the sample x under the j-th Gaussian componentk The value of the probability density function.

[0017] M-step: According to the maximum likelihood method for parameter estimation problems, calculate the estimated values of the parameters to be determined:

[0018]

[0019] where: M is the number of samples x k ; γ i is the result of summing each probability γ ki over the samples, which can be expressed as:

[0020]

[0021] Repeat the iterative calculations of the above two steps, namely the E-step and the M-step, until the results of the parameters to be determined converge, then the maximum likelihood solution of the parameters of the multivariate Gaussian mixture model can be obtained, and thus the source-load non-parametric probability distribution can be obtained.

[0022] Furthermore, based on the construction of a simplified model of system operation for the linearization of AC power flow in a power system, the specific method is as follows:

[0023] Construct an AC power flow model in polar coordinates in the power system, specifically:

[0024]

[0025] where, U i represents the voltage of node i; θ ij represents the phase difference between nodes i and j; G i0 and B i0 represent the shunt conductance and susceptance of node i respectively; P ij , Q ij , G ij , B ij represent the active and reactive power, conductance, and susceptance on line ij respectively.

[0026] Further study the influence of power on voltage and derive the node balance equation, specifically:

[0027]

[0028] where, P is , Q is are the active power and reactive power injected into node i respectively; P i , Q i are the active power and reactive power output from node i respectively; ΔP i , ΔQ i are the unbalanced active power and reactive power of node i respectively.

[0029] The first-order Taylor series approximation method is used to linearly expand the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution, obtaining a simplified system operation model based on the linearization of the AC power flow of the power system. The specific method is as follows:

[0030] First, select the source-load uncertainty expansion point \(x_0\) at the mean point of the source-load non-parametric probability distribution, and its calculation formula is:

[0031]

[0032] Substitute the source-load uncertainty expansion point \(x_0\) into the AC power flow model in the polar coordinate system of the power system to obtain the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point \(x_0\).

[0033] Then, take the values of the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point \(x_0\) as the Taylor expansion point, and approximate the nodal power balance equation as the following linearized form at the Taylor expansion point:

[0034]

[0035] where \(P\) i GU represents the active power output by the conventional generator at node \(i\); \(P\) i PV represents the active power output by the new energy generation at node \(i\); \(P\) i D represents the active power of the load at node \(i\); are the voltage Taylor expansion points of nodes \(i\) and \(j\) respectively; is the Taylor expansion point of the phase difference between nodes \(i\) and \(j\); \(\Delta v\) i , \(\Delta v\) j are the voltage increments of nodes \(i\) and \(j\) respectively; \(\Delta\theta\) ij is the phase difference increment between nodes \(i\) and \(j\);

[0036] Next, based on the linearized result of the nodal power balance equation, linearize the AC power flow model in the polar coordinate system of the power system. Specifically:

[0037]

[0038] Perform further analytical derivation on the linearized AC power flow model in the polar coordinate system of the power system, and the mathematical expression is specifically:

[0039]

[0040] where: M1 and M2 are the coefficients corresponding to the first-order Taylor expansion of the active and reactive powers respectively, and their mathematical meanings are:

[0041]

[0042] For the AC power flow model in polar coordinates in the linearized power system after analytical derivation, separating the new energy power, load from other variables, a simplified model of system operation based on the linearization of the AC power flow of the power system is obtained, specifically:

[0043] y = Ax + C

[0044] where y is the system power flow random variable, including the amplitude and phase angle of the node voltage, and A and C are linearization coefficients.

[0045] Furthermore, the non-parametric probability power flow mapping method for the power system is specifically:

[0046] Combining the linear transformation method of Gaussian distribution and the law of total probability, the complete probability distribution of the system power flow can be deduced.

[0047] Combining the linear transformation method of Gaussian distribution, the probability distribution of the power system power flow under each Gaussian component is obtained; the specific calculation formula for the probability distribution of the power system power flow under each Gaussian component is:

[0048] f i (y) = f N (y; Aμ i + C, AΣ i A T )

[0049] where f i (y) represents the probability distribution of the power system power flow under each Gaussian component.

[0050] Combined with the law of total probability, if the probability distribution of the random vector x conforms to the multivariate Gaussian mixture model, then regardless of whether there is a correlation between the individual random variables in the vector x, the probability distribution of the linear combination of the random variables in the vector x follows the multivariate Gaussian mixture model; therefore, the probability distributions of the power system power flow under each Gaussian component can be weighted and summed according to the weights to obtain the non-parametric probability power flow probability distribution of the power system; the non-parametric probability power flow probability distribution of the power system includes the probability distributions of the amplitude and phase angle of the node voltage.

[0051] The specific calculation formulas for the probability distributions of the node voltage amplitude and phase angle are:

[0052]

[0053] where f(y) represents the value of the probability density function of the system power flow random variable y.

[0054] The present invention also provides a non-parametric probabilistic power flow calculation device for a power system considering complex uncertainties. This device is used to execute the above-mentioned power flow calculation method, and specifically includes:

[0055] A source-load non-parametric probability distribution calculation module, which is used to obtain source-load uncertainty data based on probability prediction, sample the obtained source-load uncertainty data, screen and remove outlier data values, and perform parameter estimation of a multivariate Gaussian mixture model on the screened sampling data to obtain a source-load non-parametric probability distribution;

[0056] A system operation simplified model construction module based on the linearization of the AC power flow of the power system, which is used to construct an AC power flow model in the polar coordinate system of the power system, and perform linear expansion of the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution by using the first-order Taylor series approximation method to obtain a system operation simplified model based on the linearization of the AC power flow of the power system;

[0057] A non-parametric probabilistic power flow probability distribution calculation module for the power system, which is used to obtain the probability distribution of the power flow distribution of the power system under each Gaussian component based on the system operation simplified model based on the linearization of the AC power flow of the power system and in combination with the linear transformation method of the Gaussian distribution; according to the total probability law, perform weighted summation of the probability distributions of the power flow distribution of the power system under each Gaussian component by weight to obtain the non-parametric probabilistic power flow probability distribution of the power system.

[0058] The present invention also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned power flow calculation method.

[0059] The present invention also provides a computer-readable storage medium, on which computer instructions are stored, and the computer instructions are used to cause a computer to execute the steps of the above-mentioned power flow calculation method.

[0060] The beneficial effects of the present invention are:

[0061] A non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties of the present invention proposes a method for constructing a source-load non-parametric probability distribution based on a multivariate Gaussian mixture model, and proposes a simplified system operation model based on the linearization of the AC power flow of the power system. On this basis, non-parametric probability mapping is performed, and combined with the linear transformation method of the Gaussian distribution, the probability distribution of the power flow distribution of the power system under each Gaussian component is obtained. According to the law of total probability, the complete non-parametric probabilistic power flow distribution of the power system is obtained. Compared with the traditional probabilistic power flow technology based on probability distribution assumptions, the non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties proposed by the present invention considers the correlation and non-parametric distribution characteristics of complex random variables, has stronger generalization ability and accuracy, and has important reference significance for quantifying the operation uncertainty of power systems under complex uncertainties. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flowchart of the non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] An embodiment of the present invention provides a non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties, and the process of this method is as Figure 1 shown. Specifically, this method includes:

[0064] Constructing a source-load non-parametric probability distribution based on a multivariate Gaussian mixture model: obtaining source-load uncertainty data based on probability prediction, sampling the obtained source-load uncertainty data, screening and removing outlier data values, and performing parameter estimation of the multivariate Gaussian mixture model on the screened sampling data to obtain the source-load non-parametric probability distribution;

[0065] Constructing a simplified system operation model based on the linearization of the AC power flow of the power system: constructing an AC power flow model in the polar coordinate system of the power system, and performing linear expansion on the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution by using the first-order Taylor series approximation method to obtain the simplified system operation model based on the linearization of the AC power flow of the power system;

[0066] Performing non-parametric probability mapping on the power flow distribution of the power system: on the basis of the simplified system operation model based on the linearization of the AC power flow of the power system, combining the linear transformation method of the Gaussian distribution to obtain the probability distribution of the power flow distribution of the power system under each Gaussian component; according to the law of total probability, performing weighted summation of the probability distributions of the power flow distribution of the power system under each Gaussian component by weights to obtain the non-parametric probabilistic power flow probability distribution of the power system.

[0067] The multi-variate Gaussian mixture model can fit probability distributions of any distribution form and has non-parametric probability characteristics. The specific expression of the probability density function of the multi-variate Gaussian mixture model is as follows:

[0068]

[0069] Among them, x represents the random vector composed of the filtered new energy power and load; f GMM (x|Θ) represents the probability density function value of the random variable described by the multi-variate Gaussian mixture model; f N (x; μ i , Σ i ) represents the i-th Gaussian component in the multi-variate Gaussian mixture model; ω i , μ i and Σ i represent the weight, mean vector and covariance matrix of the i-th Gaussian component respectively; n is the number of Gaussian components in the multi-variate Gaussian mixture model; Θ is the parameter set to be solved, and its expression is:

[0070]

[0071] Among them, the value of the parameter set Θ to be solved is usually calculated by the expectation maximization algorithm, which can be specifically divided into two steps:

[0072] E-step (E-step): Calculate the probability that the data comes from each Gaussian component according to the current parameter values. Let the probability that the sample x k in x comes from the i-th Gaussian component be γ ki , and its calculation formula is:

[0073]

[0074] Among them, f N (x k ; μ i , Σ i ) represents the probability density function value of the sample x k under the i-th Gaussian component; f N (x k ; μ j , Σ j ) represents the probability density function value of the sample x k under the j-th Gaussian component.

[0075] M-step (M-step): Calculate the estimated value of the parameter to be solved according to the maximum likelihood method of the parameter estimation problem:

[0076]

[0077] In the formula: M is the number of samples x k ; γi For each probability γ ki The result of summing according to the samples can be expressed as:

[0078]

[0079] Repeat the calculation of the above two steps of the E-step and the M-step until the result of the parameter to be solved converges, and the maximum likelihood solution of the parameters of the multivariate Gaussian mixture model can be obtained, and the source-load non-parametric probability distribution can be obtained.

[0080] The construction of the simplified model of system operation based on the linearization of the AC power flow of the power system is specifically as follows:

[0081] Construct the AC power flow model in the polar coordinate system in the power system, specifically:

[0082]

[0083] where U i represents the voltage of node i; θ ij represents the phase difference between nodes i and j; G i0 and B i0 respectively represent the ground conductance and susceptance of node i; P ij , Q ij , G ij , B ij respectively represent the active and reactive powers, conductance, and susceptance on line ij.

[0084] Further study the influence of power on voltage and derive the node balance equation, specifically:

[0085]

[0086] where P is , Q is are respectively the active power and reactive power injected into node i; P i , Q i are respectively the active power and reactive power output from node i; ΔP i , ΔQ i are respectively the unbalanced active power and reactive power of node i.

[0087] Use the first-order Taylor series approximation method to linearly expand the AC power flow model in the polar coordinate system in the power system at the mean point of the source-load non-parametric probability distribution to obtain the simplified model of system operation based on the linearization of the AC power flow of the power system; the specific method is:

[0088] First, select the source-load uncertainty expansion point x0 at the mean point of the source-load non-parametric probability distribution, and its calculation formula is:

[0089]

[0090] Substitute the source-load uncertainty expansion point \(x_0\) into the AC power flow model in the polar coordinate system of the power system to obtain the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point \(x_0\).

[0091] Then, using the values of the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point \(x_0\) as the Taylor expansion point, approximate the nodal power balance equation at the Taylor expansion point as the following linearized form:

[0092]

[0093] where \(P\) i GU represents the active power output by the conventional generator at node \(i\); \(P\) i PV represents the active power output by the new energy generation at node \(i\); \(P\) i D represents the active power of the load at node \(i\); are the Taylor expansion points of the voltages at nodes \(i\) and \(j\) respectively; is the Taylor expansion point of the phase difference between nodes \(i\) and \(j\); \(\Delta v\) i , \(\Delta v\) j are the voltage increments at nodes \(i\) and \(j\) respectively; \(\Delta\theta\) ij is the phase difference increment between nodes \(i\) and \(j\);

[0094] Next, based on the linearized result of the nodal power balance equation, linearize the AC power flow model in the polar coordinate system of the power system, specifically:

[0095]

[0096] Perform further analytical derivation on the linearized AC power flow model in the polar coordinate system of the power system. The mathematical expression is specifically:

[0097]

[0098] In the formula: \(M_1\) and \(M_2\) are the coefficients corresponding to the first-order Taylor expansion of the active and reactive powers respectively, and the mathematical meanings are:

[0099]

[0100] For the linearized AC power flow model in the polar coordinate system of the power system after analytical derivation, separate the new energy power, load, and other variables to obtain a simplified system operation model based on the linearization of the AC power flow of the power system, specifically:

[0101] y = Ax + C

[0102] Wherein, y is the random variable of the system power flow, including the amplitude and phase angle of the node voltage, and A and C are linearization coefficients.

[0103] A non-parametric probability power flow mapping method for a power system, specifically:

[0104] Combining the linear transformation method of the Gaussian distribution and the law of total probability, the complete probability distribution of the system power flow can be derived.

[0105] Combining the linear transformation method of the Gaussian distribution, the probability distribution of the power system power flow under each Gaussian component is obtained; the specific calculation formula for the probability distribution of the power system power flow under each Gaussian component is:

[0106] f i (y) = f N (y; Aμ i + C, AΣ i A T )

[0107] In the formula, f i (y) represents the probability distribution of the power system power flow under each Gaussian component.

[0108] Based on the law of total probability, weighted summation is performed on each Gaussian component of the Gaussian mixture model, and it can be obtained that: if the probability distribution of the random vector x conforms to the multivariate Gaussian mixture model, then regardless of whether there is a correlation between the individual random variables in the vector x, the probability distribution of the linear combination of the random variables in the vector x follows the multivariate Gaussian mixture model; therefore, the probability distributions of the power system power flow under each Gaussian component can be weighted and summed according to the weights to obtain the non-parametric probability power flow probability distribution of the power system; the non-parametric probability power flow probability distribution of the power system includes the probability distributions of the amplitude and phase angle of the node voltage.

[0109] The specific calculation formulas for the probability distributions of the node voltage amplitude and phase angle are:

[0110]

[0111] Wherein, f(y) represents the value of the probability density function of the system power flow random variable y.

[0112] Another embodiment of the present invention also provides a non-parametric probability power flow calculation device for a power system considering complex uncertainties, and this device includes:

[0113] A source-load non-parametric probability distribution calculation module, which is used to obtain source-load uncertainty data based on probability prediction, sample the obtained source-load uncertainty data, filter out outlier data values, and perform parameter estimation of a multivariate Gaussian mixture model on the filtered sampled data to obtain a source-load non-parametric probability distribution;

[0114] A system operation simplified model construction module based on the linearization of the AC power flow of the power system, which is used to construct an AC power flow model in the polar coordinate system of the power system, and linearly expand the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution by using the first-order Taylor series approximation method to obtain a system operation simplified model based on the linearization of the AC power flow of the power system;

[0115] A non-parametric probability power flow probability distribution calculation module of the power system, which is used to obtain the probability distribution of the power flow distribution of the power system under each Gaussian component based on the system operation simplified model based on the linearization of the AC power flow of the power system and in combination with the linear transformation method of the Gaussian distribution; according to the law of total probability, the probability distributions of the power flow distribution of the power system under each Gaussian component are weighted and summed to obtain the non-parametric probability power flow probability distribution of the power system.

[0116] Among them, the expression of the probability density function of the multivariate Gaussian mixture model is:

[0117]

[0118] Among them, x represents the random vector composed of the new energy power and load after screening; f GMM (x|Θ) represents the probability density function value of the random variable described by the multivariate Gaussian mixture model; f N (x; μ i , Σ i ) represents the i-th Gaussian component in the multivariate Gaussian mixture model; ω i , μ i and Σ i respectively represent the weight, mean vector and covariance matrix of the i-th Gaussian component; n is the number of Gaussian components in the multivariate Gaussian mixture model; Θ is the set of parameters to be solved, and its expression is:

[0119]

[0120] Among them, the value of the set of parameters to be solved Θ is calculated by using the expectation maximization algorithm, which is specifically divided into two steps:

[0121] E step: Calculate the probability that the data comes from each Gaussian component according to the current parameter value; assume that the probability that the sample x k in x comes from the i-th Gaussian component is γ ki , and its calculation formula is:

[0122]

[0123] Among them, f N (x k ; μ i , Σ i ) represents the value of the probability density function of the sample x k under the i-th Gaussian component; f N (x k ; μ j , Σ j ) represents the value of the probability density function of the sample x k under the j-th Gaussian component;

[0124] M step: According to the maximum likelihood method of the parameter estimation problem, calculate the estimated values of the parameters to be solved:

[0125]

[0126] In the formula: M is the number of samples x k ; γ i is the result of summing each probability γ ki according to the samples, expressed as:

[0127]

[0128] Repeat the calculation of these two steps of the E step and the M step until the result of the parameter to be solved converges, then the maximum likelihood solution of the parameters of the multivariate Gaussian mixture model can be obtained, and the source-load non-parametric probability distribution can be obtained.

[0129] The construction of the AC power flow model in the polar coordinate system in the power system is specifically as follows:

[0130]

[0131] Among them, U i represents the voltage of node i; θ ij represents the phase difference between node i and j; G i0 and B i0 respectively represent the shunt conductance and susceptance of node i; P ij , Q ij , G ij , B ij respectively represent the active and reactive powers, conductance, and susceptance on line ij;

[0132] Further study the influence of power on voltage and derive the node balance equation, specifically as follows:

[0133]

[0134] Among them, P is , Qis The active power and reactive power injected into node i respectively; P i , Q i The active power and reactive power output from node i respectively; ΔP i , ΔQ i The unbalanced active power and reactive power of node i respectively;

[0135] The above-mentioned first-order Taylor series approximation method is used to linearly expand the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution, and a simplified system operation model based on the linearization of the AC power flow of the power system is obtained; the specific method is as follows:

[0136] First, select the source-load uncertainty expansion point x0 at the mean point of the source-load non-parametric probability distribution, and its calculation formula is:

[0137]

[0138] Substitute the active power P corresponding to the source-load uncertainty expansion point x0 ij into the AC power flow model in the polar coordinate system of the power system to obtain the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point x0

[0139] Then, take the values of the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point x0 as the Taylor expansion point, and approximate the node balance equation at the Taylor expansion point as the following linearized form:

[0140]

[0141] Among them, P i GU represents the active power output by the conventional generator of node i; P i PV represents the active power output by the new energy power generation of node i; P i D represents the active power of the load of node i; are the voltage Taylor expansion points of nodes i and j respectively; is the Taylor expansion point of the phase difference between nodes i and j; Δv i , Δv j are the voltage increments of nodes i and j respectively; Δθ ij is the phase difference increment between nodes i and j;

[0142] Next, based on the linearization result of the node balance equation, linearize the AC power flow model in the polar coordinate system of the power system, specifically:

[0143]

[0144] Further analytical derivation is carried out on the AC power flow model in polar coordinates in the linearized power system, specifically as follows:

[0145]

[0146] In the formula, M1 and M2 are the coefficients corresponding to the active and reactive powers after the first-order Taylor expansion, respectively, and are specifically calculated through the following formula:

[0147]

[0148] Finally, for the AC power flow model in polar coordinates in the linearized power system after the analytical derivation, the new energy power, load and other variables are separated to obtain the simplified system operation model based on the linearization of the power system AC power flow, specifically as follows:

[0149] y = Ax + C

[0150] Among them, y is the system power flow random variable, including the amplitude and phase angle of the node voltage; A and C are the linearization coefficients.

[0151] The calculation formula for the probability distribution of the power system power flow distribution under each Gaussian component is specifically as follows:

[0152] f i (y) = f N (y; Aμ i + C, AΣ i A T )

[0153] Among them, f i (y) represents the probability distribution of the power system power flow distribution under each Gaussian component;

[0154] The non-parametric probability power flow probability distribution of the power system includes the probability distributions of the node voltage amplitude and phase angle;

[0155] The calculation formulas for the probability distributions of the node voltage amplitude and phase angle are specifically as follows:

[0156]

[0157] Among them, f(y) represents the value of the probability density function of the system power flow random variable y.

[0158] Another embodiment of the present invention provides an electronic device. The electronic device includes: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned power flow calculation method.

[0159] Another embodiment of the present invention provides a computer-readable storage medium. Computer instructions are stored on the computer-readable storage medium, and the computer instructions are used to cause a computer to execute the steps of the above-mentioned power flow calculation method.

Claims

1. A non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties, characterized in that, Including: Based on probability prediction, obtain source-load uncertainty data, sample the obtained source-load uncertainty data, screen and remove outlier data values, and perform parameter estimation of the multivariate Gaussian mixture model on the screened sampled data to obtain the source-load non-parametric probability distribution; Construct an AC power flow model in the polar coordinate system of the power system, and use the first-order Taylor series approximation method to linearly expand the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution to obtain a simplified system operation model based on the linearization of the power system AC power flow; Based on the simplified system operation model based on the linearization of the power system AC power flow, combine the linear transformation method of the Gaussian distribution to obtain the probability distribution of the power system power flow distribution under each Gaussian component; according to the law of total probability, weight and sum the probability distributions of the power system power flow distribution under each Gaussian component to obtain the non-parametric probability power flow probability distribution of the power system.

2. The non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties according to claim 1, characterized in that The probability density function expression of the multivariate Gaussian mixture model is: Among them, \(x\) represents a random vector composed of the filtered new - energy power and load; \(f\) GMM (x|\Theta)\) represents the probability density function value of a random variable described by a multivariate Gaussian mixture model; \(f\) N (x;\mu i ,\Sigma i ) represents the \(i\) - th Gaussian component in the multivariate Gaussian mixture model; \(\omega i ,\mu i and \(\Sigma i respectively represent the weight, mean vector and covariance matrix of the \(i\) - th Gaussian component; \(n\) is the number of Gaussian components in the multivariate Gaussian mixture model; \(\Theta\) is the parameter set to be solved, and its expression is: Among them, the value of the parameter set Θ to be solved is calculated using the expectation maximization algorithm, which is specifically divided into two steps: Step E: Calculate the probabilities that the data comes from each Gaussian component according to the current parameter values; assume that the sample x in x k The probability of coming from the i-th Gaussian component is γ ki , and its calculation formula is: where, f N (x k ; μ i , Σ i ) represents the probability density function value of the sample x k under the i-th Gaussian component; f N (x k ; μ j , Σ j ) represents the probability density function value of the sample x k under the j-th Gaussian component; M step: According to the maximum likelihood method of the parameter estimation problem, calculate the estimated value of the parameter to be solved: where: M is the number of samples x k ; γ i is the result of summing each probability γ ki by sample, expressed as: Repeat the calculation of these two steps of the E step and the M step until the result of the parameter to be solved converges, and then the maximum likelihood solution of the parameters of the multivariate Gaussian mixture model can be obtained, and the source-load non-parametric probability distribution can be obtained.

3. The non-parametric probabilistic power flow calculation method for a power system considering complex uncertainties according to claim 2, wherein Construct an AC power flow model in the polar coordinate system of the power system, specifically: Among them, U i represents the voltage of node i; θ ij represents the phase difference between nodes i and j; G i0 and B i0 respectively represent the shunt conductance and susceptance of node i to the ground; P ij , Q ij , G ij , B ij respectively represent the active and reactive power, conductance, and susceptance on line ij; Further study the influence of power on voltage, and derive the node balance equation, specifically: Among them, P is , Q is are the active power and reactive power injected into node i respectively; P i , Q i are the active power and reactive power output from node i respectively; ΔP i , ΔQ i are the unbalanced active power and reactive power of node i respectively; Use the first-order Taylor series approximation method to linearly expand the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution to obtain a simplified system operation model based on the linearization of the power system AC power flow; the specific method is: First, select the source-load uncertainty expansion point x0 at the mean point of the source-load non-parametric probability distribution, and its calculation formula is: Substitute the active power P corresponding to the source-load uncertainty expansion point x0 ij into the AC power flow model in the polar coordinate system of the power system to obtain the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point x0 Then, use the values of the voltage magnitude and phase angle corresponding to the source-load uncertainty expansion point x0 as the Taylor expansion point, and approximate the nodal balance equation at the Taylor expansion point as the following linearized form: Among them, P i GU represents the active power output of the conventional generator at node i; P i PV represents the active power output of the new energy generation at node i; P i D represents the active power of the load at node i; are the voltage Taylor expansion points of nodes i and j respectively; is the Taylor expansion point of the phase difference between nodes i and j; Δv i , Δv j are the voltage increments of nodes i and j respectively; Δθ ij is the phase difference increment between nodes i and j; Then, based on the linearization result of the node balance equation, linearly expand the AC power flow model in the polar coordinate system of the power system, specifically: Perform further analytical derivation on the linearly expanded AC power flow model in the polar coordinate system of the power system, specifically: In the formula, M1 and M2 are the coefficients corresponding to the active power and reactive power after the first-order Taylor expansion, respectively, and are specifically calculated by the following formula: Finally, for the linearly expanded AC power flow model in the polar coordinate system of the power system after analytical derivation, separate the new energy power, load and other variables to obtain the simplified system operation model based on the linearization of the power system AC power flow, specifically: y = Ax + C Among them, y is the system power flow random variable, including the amplitude and phase angle of the node voltage; A and C are the linearization coefficients.

4. The non-parametric probabilistic power flow calculation method for power systems considering complex uncertainties according to claim 3, characterized in that The calculation formula of the probability distribution of the power system power flow distribution under each Gaussian component is specifically: f i (y) = f N (y; Aμ i + C, AΣ i A T ) Among them, f i (y) represents the probability distribution of the power flow distribution in the power system under each Gaussian component; The non-parametric probability power flow probability distribution of the power system includes the probability distributions of the node voltage amplitude and phase angle; The calculation formulas of the probability distributions of the node voltage amplitude and phase angle are specifically: Among them, f(y) represents the probability density function value of the system power flow random variable y.

5. A non-parametric probabilistic power flow calculation device for a power system considering complex uncertainties, characterized in that, It includes: A source-load non-parametric probability distribution calculation module, which is used to obtain source-load uncertainty data based on probability prediction, sample the obtained source-load uncertainty data, screen out and remove outlier data values, and perform parameter estimation of the multivariate Gaussian mixture model on the screened sampling data to obtain the source-load non-parametric probability distribution; A system operation simplified model construction module based on the linearization of the AC power flow of the power system, which is used to construct an AC power flow model in the polar coordinate system of the power system, and perform linear expansion on the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution by using the first-order Taylor series approximation method to obtain a system operation simplified model based on the linearization of the AC power flow of the power system; A non-parametric probability power flow probability distribution calculation module of the power system, which is used to obtain the probability distribution of the power system power flow under each Gaussian component based on the system operation simplified model based on the linearization of the AC power flow of the power system and in combination with the linear transformation method of the Gaussian distribution; according to the total probability law, perform weighted summation of the probability distributions of the power system power flow under each Gaussian component by weight to obtain the non-parametric probability power flow probability distribution of the power system.

6. The non-parametric probabilistic power flow calculation device for a power system considering complex uncertainties according to claim 5, characterized in that The probability density function expression of the multivariate Gaussian mixture model is: where \(x\) represents the random vector composed of the filtered new - energy power and load; \(f\) GMM (x|\Theta)\) represents the probability density function value of the random variable described by the multi - variate Gaussian mixture model; \(f\) N (x;\mu i ,\(\Sigma\) i ) represents the \(i\) - th Gaussian component in the multi - variate Gaussian mixture model; \(\omega\) i ,\(\mu\) i and \(\Sigma\) i respectively represent the weight, mean vector and covariance matrix of the \(i\) - th Gaussian component; \(n\) is the number of Gaussian components in the multi - variate Gaussian mixture model; \(\Theta\) is the parameter set to be solved, and its expression is: Among them, the value of the parameter set Θ to be solved is calculated by using the expectation maximization algorithm, which is specifically divided into two steps: Step E: Calculate the probability that the data comes from each Gaussian component according to the current parameter values; assume that the sample x in x k The probability of coming from the i-th Gaussian component is γ ki , and its calculation formula is: where, f N (x k ; μ i , Σ i ) represents the probability density function value of the sample x k under the i-th Gaussian component; f N (x k ; μ j , Σ j ) represents the probability density function value of the sample x k under the j-th Gaussian component; M step: According to the maximum likelihood method of the parameter estimation problem, calculate the estimated value of the parameter to be solved: Where: M is the number of samples x k ; γ i is the result of summing each probability γ ki by sample, expressed as: Repeat the calculation of these two steps of the E step and the M step until the result of the parameter to be solved converges, and then the maximum likelihood solution of the parameters of the multivariate Gaussian mixture model can be obtained, and the source-load non-parametric probability distribution can be obtained.

7. The non-parametric probabilistic power flow calculation device for a power system considering complex uncertainties according to claim 6, wherein The construction of the AC power flow model in the polar coordinate system of the power system is specifically: Among them, U i represents the voltage of node i; θ ij represents the phase difference between nodes i and j; G i0 and B i0 respectively represent the ground conductance and susceptance of node i; P ij , Q ij , G ij , B ij respectively represent the active and reactive power, conductance, and susceptance on line ij; Further study the influence of power on voltage, and derive the node balance equation, specifically: Among them, P is , Q is are the active power and reactive power injected into node i respectively; P i , Q i are the active power and reactive power output from node i respectively; ΔP i , ΔQ i are the unbalanced active power and reactive power of node i respectively; The first-order Taylor series approximation method is used to perform linear expansion on the AC power flow model in the polar coordinate system of the power system at the mean point of the source-load non-parametric probability distribution to obtain a system operation simplified model based on the linearization of the AC power flow of the power system; the specific method is: First, select the source-load uncertainty expansion point x0 at the mean point of the source-load non-parametric probability distribution, and its calculation formula is: Substitute the active power P corresponding to the source-load uncertainty expansion point x0 ij into the AC power flow model in the polar coordinate system of the power system to obtain the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point x0 Then, use the values of the voltage amplitude and phase angle corresponding to the source-load uncertainty expansion point x0 as the Taylor expansion point, and approximate the nodal balance equation at the Taylor expansion point as the following linearized form: Among them, P i GU represents the active power output of the conventional generator at node i; P i PV represents the active power output of the new energy power generation at node i; P i D represents the active power of the load at node i; are the voltage Taylor expansion points of nodes i and j respectively; is the Taylor expansion point of the phase difference between nodes i and j; Δv i , Δv j are the voltage increments of nodes i and j respectively; Δθ ij is the phase difference increment between nodes i and j; Next, based on the linearization result of the node balance equation, perform linearization on the AC power flow model in the polar coordinate system of the power system, specifically: Perform further analytical derivation on the linearized AC power flow model in the polar coordinate system of the power system, specifically: In the formula, M1 and M2 are the coefficients corresponding to the active power and reactive power after the first-order Taylor expansion respectively, and are specifically calculated by the following formula: Finally, for the linearized AC power flow model in the polar coordinate system of the power system after analytical derivation, separate the new energy power, load and other variables to obtain the system operation simplified model based on the linearization of the AC power flow of the power system, specifically: y = Ax + C Among them, y is the system power flow random variable, including the amplitude and phase angle of the node voltage; A and C are linearization coefficients.

8. The non-parametric probabilistic power flow calculation device for power systems considering complex uncertainties according to claim 7, characterized in that The specific calculation formula for the probability distribution of the power flow distribution of the power system under each Gaussian component is as follows: f i (y) = f N (y; Aμ i + C, AΣ i A T ) where f i (y) represents the probability distribution of the power flow distribution in the power system under each Gaussian component; The non-parametric probability power flow probability distribution of the power system includes the probability distributions of the node voltage amplitude and phase angle; The specific calculation formulas for the probability distributions of the node voltage amplitude and phase angle are as follows: Among them, f(y) represents the probability density function value of the system power flow random variable y.

9. An electronic device, characterized in that, Including: One or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1-4.

10. A computer-readable storage medium having computer instructions stored thereon, characterized in that, The computer instructions are used to cause the computer to execute the steps of the method according to any one of claims 1-4.

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