A quantitative assessment and risk control method for the impact of distributed photovoltaic access

Abstract

This invention discloses a method for quantitatively assessing and controlling the impact of distributed photovoltaic access, belonging to the field of distribution network optimization methods. Based on historical data on node load power and solar radiation intensity, as well as the photovoltaic installation status or access plan of the distribution network, a Gaussian mixture model of node injection power is generated. Through linearized power flow calculation, the probability density functions of electrical quantities such as node voltage amplitude and branch active power are quickly obtained, thereby assessing the impact of distributed photovoltaic access. Based on the proposed quantitative assessment method for the impact of distributed photovoltaic grid connection, a method for calculating the photovoltaic carrying capacity margin of any node in the distribution network is proposed. The maximum photovoltaic grid-connected capacity of a node in the distribution network can be obtained under a certain risk probability, providing effective guidance for the power grid.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network optimization methods, and specifically relates to a method for quantitatively evaluating the impact of distributed photovoltaic access and controlling risks. Background Art

[0002] With the successive release of policies and technical standards related to photovoltaic power generation, China's grid-connected photovoltaic capacity has shown a sharp upward trend in recent years. The integration of large-scale distributed photovoltaics has, on the one hand, caused changes in the direction of system power flows, affecting system voltage and power distribution, and resulting in voltage and power flow violations. On the other hand, the impact of distributed photovoltaics on the operation of the distribution network varies in different scenarios, making traditional single assessment methods difficult to accurately characterize the multi-dimensional risks of the system. Therefore, new methods are urgently needed to more accurately quantify the impact of distributed photovoltaic integration on the distribution network.

[0003] Compared to traditional analysis models, the Gaussian mixture model can analyze the spatiotemporal relationships between the coupled outputs of distributed photovoltaic power plants connected to a region from multiple dimensions. Based on these characterizations, a more precise analysis of the impact of distributed photovoltaic grid integration on distribution network areas can be performed. Therefore, this paper proposes a method for quantitatively analyzing and risk-controlling the impact of distributed photovoltaic integration on distribution networks based on the Gaussian mixture model. Summary of the Invention

[0004] In order to solve the technical problems existing in the background technology, the present invention aims to provide a method for quantitative assessment and risk control of the impact of distributed photovoltaic access.

[0005] In order to solve the technical problem, the technical solution of the present invention is:

[0006] A method for quantitative assessment and risk control of impacts of distributed photovoltaic access, comprising:

[0007] Based on the historical data of load power at distribution network nodes, historical data of solar irradiation intensity, and the photovoltaic installation status or access plan of the distribution network, a Gaussian mixture model of node injection power is constructed;

[0008] A linearized power flow model for the distribution network is constructed. The uncertainty of node injection power is determined based on a Gaussian mixture model. The probability density function of node voltage amplitude and branch active power is obtained through probabilistic power flow calculation to quantitatively evaluate the impact of distributed photovoltaic access.

[0009] Based on the quantitative assessment results of the impact of distributed photovoltaic grid connection, the photovoltaic carrying capacity margin of any node in the distribution network is calculated, and the maximum photovoltaic grid-connected capacity of any node in the distribution network under the risk probability is obtained.

[0010] Furthermore, based on the historical data of distribution network node load power, historical data of solar radiation intensity, and photovoltaic installation conditions or access plans of the distribution network, the historical data of node injection power are calculated, and a Gaussian mixture model of node injection power is constructed using the historical data of node injection power.

[0011] Furthermore, the uncertainty of distributed photovoltaic power generation is characterized, and it is determined that the distributed photovoltaic output of the same distribution area obeys the same distribution. For a given distributed photovoltaic access scheme, that is, the distributed photovoltaic access location and capacity are both known, the distributed photovoltaic output corresponding to each node can be obtained according to formula (1):

[0012]

[0013] Where: η is the conversion efficiency of the photovoltaic inverter; P PV,i is the distributed photovoltaic installation capacity at node i;

[0014] P in,i (t) = P PV,i (t)-P load,i (t) (2)

[0015] Where: P in,i (t) is the injected power at node i at time t; P load,i (t) is the load power at node i at time t;

[0016] Based on the one-year statistical data of node load and light irradiation intensity in the distribution station area, a statistical analysis is performed on the node load data and light irradiation intensity data within each hour. The data of the injected power of each node within each hour is generated, and the PDF of the joint injected power of the nodes in the corresponding period is obtained, that is, the historical data of the node injected power is obtained.

[0017] Furthermore, constructing a Gaussian mixture model of node injection power includes:

[0018] The random variable that determines the node injection power is X, and its probability distribution is represented by the superposition of several Gaussian distributions:

[0019]

[0020]

[0021] Where: f X (x) is the joint probability density function of the random variable X; ω m is the weight coefficient; W is the dimension of X; N m Represents a multidimensional normal distribution, which is called the mth Gaussian component of the Gaussian mixture model GMM; det is the determinant of the matrix; M is the total number of Gaussian components; μ m and σm are the mean vector and covariance matrix of the mth Gaussian component respectively;

[0022] In order to solve the Gaussian mixture model shown in equation (3), it is necessary to further determine the unknown parameters ω of each Gaussian component: m 、μ m and σ m , so that the Gaussian mixture model is closest to the actual sample obtained, and the parameters to be determined can be obtained by the maximum likelihood estimation method.

[0023] Furthermore, the maximum likelihood estimation includes:

[0024] Solving GMM using maximum likelihood estimation requires finding the likelihood function and then solving the joint probability distribution of the sample set. First, introduce the latent variable γ to represent the probability of selecting the mth Gaussian component in each sampling. The latent variable γ is a binary random variable with a dimension of M. There is only a specific element γ in any dimension. m The value is non-zero, which is represented by

[0025] f Γ (γ m =1) =ω m (5)

[0026] Where: f(γ m =1) indicates γ m The probability of taking the value 1;

[0027] First, determine the latent variable γ, sample from a specific Gaussian distribution, and obtain the conditional probability distribution of the sample x that obeys the Gaussian distribution:

[0028] f X|Γ (x|γ m =1)=N m (x; μ m ,σ m ) (6)

[0029] Then the probability density function of a sample x containing m Gaussian components is:

[0030]

[0031] The joint probability density function of the random variable X sample set is:

[0032]

[0033] Where: N is the number of samples;

[0034] Its log-likelihood function is:

[0035]

[0036] By taking the derivative of formula (9), we can get the parameters of the Gaussian mixture model (ω, μ, σ); there is a summation sign in the logarithm in formula (9), so the maximum expectation algorithm EM is introduced for improvement: the EM algorithm includes E step and M step;

[0037] 1) Step E:

[0038] In the sample set X=(x1,x2,…,x n ,…,x N ) introduces the hidden variable γ n,m , represents the sample x n It is sampled from the mth Gaussian component, and the sample is expanded to obtain the complete data set:

[0039] (x n ; γ n,1 ,γ n,2 ,…,γ n,M ) n∈[1,N] and n∈N * (10)

[0040] To determine: ① which Gaussian component generates the nth sample; ② if the sample is generated by the mth Gaussian component, the probability that the Gaussian component generates the nth sample, the likelihood function is introduced:

[0041]

[0042] Taking m=1 as an example, the derivation process is:

[0043]

[0044] The likelihood function for non-missing data is expressed as:

[0045]

[0046] To maximize ln f X,Γ (x,γ;ω,μ,σ), select the Q function and maximize it:

[0047]

[0048] Among them, the estimate of γ E(γ n,m x n ;ω i ,μ i ,σ i ) can be further expressed as:

[0049]

[0050] 2) M step

[0051] Based on the Q function, the model parameters for the next iteration are obtained with the goal of maximizing Q.

[0052] ω i+1 ,μ i+1 ,σ i+1 =argmaxQ(ω,μ,σ;ω i ,μ i ,σ i ) (16)

[0053] Let the first-order derivative of the Q function be zero, and we get:

[0054]

[0055] Where: ω i+1 、μ i+1 and σ i+1 are the weight, mean and covariance matrix of the m-th class sample at the i+1th iteration respectively.

[0056] Furthermore, a linearized power flow model of the distribution network is constructed, which specifically includes:

[0057] Based on the linear power flow model, the AC power flow equation in the form of node injection power is:

[0058]

[0059] Where: i, j are node numbers; N is the number of nodes; U i 、U j are the voltage amplitudes of nodes i and j respectively; P i , Q i are the active power and reactive power injected at node i respectively; θ ij is the voltage phase angle difference between nodes i and j; G ij 、B ij is the element in the node admittance matrix.

[0060] The approximate assumption shown in formula (19) is adopted. This approximation has been proven to be good at approximating line power flows in two typical cases (high R / X ratio and low R / X ratio).

[0061] g ij U i (U i -U j cosθ ij )≈g ij U i (U i -U j )

[0062] =g ij (1+ΔU i )(ΔUi -ΔU j )

[0063] ≈g ij (ΔU i -ΔU j )

[0064] =g ij (U i -U j ) (19)

[0065] This approximation allows the voltage amplitude and phase angle to be decoupled, as shown in equation (2):

[0066]

[0067] Similarly, we can get:

[0068]

[0069] The line flow P can also be easily obtained from formula (2): ij The linear expression of

[0070] P ij =g ij (U i -U j )-b ij (θ i -θ j ) (twenty two)

[0071] The matrix form of formula (2) and formula (2) is shown in formula (2):

[0072]

[0073] In formula (2), both θ and U are composed of three sub-vectors, corresponding to the Vθ node (balance node), PV node, and PQ node, respectively. Arranging these nodes in the order of Vθ, PV, and PQ yields:

[0074]

[0075]

[0076] Wherein, subscripts R, S, and L correspond to the Vθ node, PV node, and PQ node, respectively.

[0077] Arranging the node admittance matrix in the same way yields:

[0078]

[0079] According to the known parameters θ of Vθ node, PV node and PQ node R , UR and U S , transform formula (2) into the following form:

[0080]

[0081] in:

[0082]

[0083]

[0084]

[0085] U=U L (29)

[0086] Performing basic row transformation on equation (26) yields:

[0087]

[0088]

[0089] Combining the first part of Equation (30) and the second part of Equation (31) into one equation can achieve the decoupling of voltage amplitude and phase angle, as shown in Equation (32):

[0090]

[0091] in:

[0092] H=H-NL -1 M (33)

[0093] L=L-MH -1 N (34)

[0094] According to formula (32), the expressions of node voltage amplitude and phase angle are as follows:

[0095]

[0096] U=L -1 QL -1 MH -1 P (36).

[0097] Furthermore, through probabilistic power flow calculation, specifically including:

[0098] The generalized equation shown in Equation (37) is used to describe the functional relationship between the node voltage and line power in the probabilistic power flow and the node injected active power:

[0099] Y=C+AX (37)

[0100] Where: X represents the node injected active power; Y represents the node voltage amplitude, phase angle and line active power and other variables; C and A represent the constant coefficient vector and matrix respectively;

[0101] Taking the node voltage amplitude as an example for derivation and verification, the node voltage amplitude obeys Gaussian distribution, and its mean phasor is Aμ m +C, the covariance matrix is ​​Aσ m A T , so the joint probability density function of the node voltage amplitude can be expressed as:

[0102]

[0103]

[0104] After multiple integration, the cumulative distribution function of the node voltage amplitude can be obtained:

[0105]

[0106] Where: Φm(y) is N m The multiple integral of (y) is expressed as:

[0107]

[0108] Furthermore, the impact of distributed photovoltaic access is quantitatively evaluated, including: utility theory and quantitative evaluation indicators of the impact of distributed photovoltaic access:

[0109] Utility Theory:

[0110] The utility theory in economics is introduced, and the utility function is used to characterize the severity. The utility function is divided into three categories according to the attitude of market participants towards risk: conservative, adventurous and neutral.

[0111] The utility function is recorded as E(W), which is a continuous function. W is the expected value of profit and loss. Its first-order derivative E'(W)>0, that is, E(W) is an increasing function of W. The second-order derivative of E(W) is E"(W):

[0112] (1) When E(W) < 0, E(W) is a convex function. At this time, the utility growth rate decreases with the increase of W, and the utility tends to saturate with the increase of W. This shows that compared with the pursuit of profit, market participants are more risk-averse and afraid of loss. Therefore, they have an averse attitude towards risk, which corresponds to a conservative utility function.

[0113] (2) When E(W) = 0, E(W) is a linear function, indicating that utility is linearly related to W and the growth rate of utility is constant, corresponding to a neutral utility function;

[0114] (3) When E(W)>0, E(W) is a concave function. At this time, the utility increases with the growth of W, and the growth rate also increases accordingly, indicating that market participants have a favorable attitude towards risk and expect to obtain greater profits, which corresponds to the risk-taking utility function.

[0115] Quantitative assessment indicators of the impact of distributed photovoltaic access:

[0116] (1) Voltage over-limit risk indicator:

[0117] The node voltage over-limit risk index is divided into the node voltage over-limit index Idx UO and node voltage exceeds lower limit indicator Idx UB The specific calculation formula of the indicator is as follows:

[0118]

[0119]

[0120] Where: K is the total sample size; s is the number of sampling times; Sev UO (U s,max ) and Sev UO (U s,min ) are the severity functions of the node voltage exceeding the upper limit and the lower limit, respectively, which are used to describe the severity of the node voltage exceeding the limit. Their definitions are shown in Equations (44) and (46):

[0121]

[0122]

[0123]

[0124]

[0125] Where: U s,i is the voltage amplitude of node i at the sth sampling time; U OV and U UV are the upper and lower limits of the node voltage respectively;

[0126] (2) Tidal current over-limit risk index:

[0127] Establishing branch power flow over-limit risk indicators in risk assessment of distribution networks containing large-scale distributed photovoltaics;

[0128] The calculation formula of the tidal current over-limit risk index is as follows:

[0129]

[0130] Where: Sev B(P s,max ) is the severity function of branch current exceeding the limit, which is used to describe the severity of branch current exceeding the limit. Its definition is shown in formula (49):

[0131]

[0132]

[0133] Where: P s,l is the active power flowing in line l at the sth sampling time; L is the total number of lines in the distribution area; P l,OV is the rated transmission power of line l;

[0134] (3) Node voltage deviation index:

[0135] The value of the node voltage deviation index can describe the distribution of node voltages in the distribution substation area. The smaller the node voltage deviation index, the more concentrated the node voltage distribution in the distribution substation area, and the better the power quality.

[0136] The calculation formula for the node voltage deviation index is as follows:

[0137]

[0138] Where: is the average value of the node voltage in the distribution area at the sth sampling time;

[0139] (4) Line loss index:

[0140] The approximate active power loss expression of the system is given as follows:

[0141]

[0142] Where: N L is the total number of branches in the distribution area; R k is the resistance of the branch k connecting node i and node j.

[0143] Furthermore, the calculation of the photovoltaic load capacity margin of any node in the distribution network includes:

[0144] Step 1: Based on the Gaussian mixture model, multiple simulations are performed on the operation of the distribution network, and the risk probability and severity faced by each node in the distribution network are obtained based on the calculation of the above indicators;

[0145] Step 2: Select the risk probability and determine that when there is a 95% probability that each node in the distribution network can maintain operation within the normal indicator range, it is determined that the distribution network can operate safely and stably at this time;

[0146] Step 3: Increase the photovoltaic grid-connected capacity of node n in the distribution network for further simulation. When the simulation results show that when the various indicators are close to the edge of their normal operating values ​​with a probability of 95%, it is determined that the photovoltaic carrying capacity of node n in the distribution network has reached its limit. The increased photovoltaic capacity Subtract the photovoltaic capacity before the increase This is the photovoltaic load capacity margin of the node:

[0147] Compared with the prior art, the advantages of the present invention are:

[0148] (1) Based on the historical data of node load power in the distribution network, the historical data of solar radiation intensity, and the photovoltaic installation status or access plan of the distribution network, a Gaussian mixture model of node injection power can be generated. Through linearized power flow calculation, the probability density function of electrical quantities such as node voltage amplitude and branch active power can be quickly obtained, thereby evaluating the impact of distributed photovoltaic access;

[0149] (2) Based on the proposed quantitative assessment method for the impact of distributed photovoltaic grid connection, a method for calculating the photovoltaic load capacity margin at any node in the distribution network is proposed. The maximum photovoltaic grid-connected capacity of a node in the distribution network under a certain risk probability can be obtained, providing effective guidance for the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0150] Figure 1 , Main flow chart of a method for quantitative assessment and risk control of impacts of distributed photovoltaic access according to the present invention. DETAILED DESCRIPTION

[0151] The specific implementation of the present invention is described below in conjunction with examples:

[0152] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0153] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" quoted in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0154] Example 1:

[0155] like Figure 1As shown, the present invention proposes a method for quantitative assessment and risk control of the impact of distributed photovoltaic access, which specifically includes the following steps:

[0156] Probabilistic power flow algorithm for distribution network based on Gaussian mixture model:

[0157] Uncertainty model of node injection power:

[0158] Affected by meteorological factors such as sunshine, wind speed, and temperature, the power generation of renewable energy sources such as distributed photovoltaics is highly random and difficult to accurately predict. Therefore, it is necessary to characterize the uncertainty of distributed photovoltaic power generation. Due to the limited spatial coverage of the distribution area, the differences in the output of each distributed photovoltaic are small. It is approximately assumed that the distributed photovoltaic output of the same distribution area follows the same distribution. For a given distributed photovoltaic access scheme, that is, the distributed photovoltaic access location and capacity are both known, the distributed photovoltaic output corresponding to each node can be obtained according to formula (1):

[0159]

[0160] Where: η is the conversion efficiency of the photovoltaic inverter; P PV,i is the distributed photovoltaic installation capacity at node i.

[0161] P in,i (t) = P PV,i (t)-P load,i (t) (2)

[0162] Where: P in,i (t) is the injected power at node i at time t; P load,i (t) is the load power at node i at time t.

[0163] Based on the one-year statistical data of node load and light irradiation intensity in the distribution station area, the node load data and light irradiation intensity data within each hour are statistically analyzed to generate the data of the injected power of each node within each hour, and thus the PDF of the joint injected power of the nodes in the corresponding period is obtained.

[0164] Most studies use typical unimodal distributions (such as normal distribution and gamma distribution) to characterize the uncertainty of photovoltaic output. However, studies have shown that photovoltaic output has the characteristics of asymmetry and multiple peaks, and the above distributions cannot represent multimodal distributions.

[0165] The Gaussian Mixture Model (GMM), as a method for analytically expressing uncertainty factors, can accurately model non-Gaussian random variables and estimate uncertainty parameters using the EM algorithm. It is suitable for characterizing the uncertainty of non-Gaussian variables in scenarios such as small sample sizes or missing data values, and has significant advantages in handling the uncertainty and correlation of non-Gaussian variables. Compared with traditional Weibull and β distribution models, GMMs possess more excellent mathematical properties, such as linear invariance, superposition, and conditional probability invariance. If the traditional power flow equation is linearized, a linearized relationship between the system operating state and the node injected power is obtained. Leveraging the linear invariance of the GMM, the probability distribution of node injected power can be analytically mapped to the joint probability distribution of the system operating state, i.e., the probabilistic power flow of the power grid.

[0166] Taking the random variable X of node injection power as an example, its probability distribution is represented by the superposition of several Gaussian distributions:

[0167]

[0168]

[0169] Where: f X (x) is the joint probability density function of the random variable X; ω m is the weight coefficient; W is the dimension of X; N m represents the multidimensional normal distribution, which is called the mth Gaussian component of GMM; det is the determinant of the matrix; M is the total number of Gaussian components; μ m and σ m are the mean vector and covariance matrix of the mth Gaussian component respectively.

[0170] In order to solve the Gaussian mixture model shown in equation (3), it is necessary to further determine the unknown parameters ω of each Gaussian component: m 、μ m and σ m , so that the Gaussian mixture model is closest to the actual sample obtained, and the parameters to be determined can be obtained by the maximum likelihood estimation method.

[0171] (1) Maximum likelihood estimation

[0172] Solving GMM using maximum likelihood estimation requires finding the likelihood function and then solving the joint probability distribution of the sample set. First, introduce the latent variable γ to represent the probability of selecting the mth Gaussian component in each sampling. The latent variable γ is a binary random variable with a dimension of M. There is only a specific element γ in any dimension. m The value is non-zero, which means:

[0173] f Γ (γm =1) =ω m (5)

[0174] Where: f(γ m =1) indicates γ m The probability of taking the value 1.

[0175] First, determine the latent variable γ, sample from a specific Gaussian distribution, and obtain the conditional probability distribution of the sample x that obeys the Gaussian distribution

[0176] f X|Γ (x|γ m =1)=N m (x; μ m ,σ m ) (6)

[0177] Then the probability density function of a sample x containing m Gaussian components is:

[0178]

[0179] The joint probability density function of the random variable X sample set is:

[0180]

[0181] Where: N is the number of samples.

[0182] Its log-likelihood function is:

[0183]

[0184] By differentiating Equation (9), we can obtain the Gaussian mixture model parameters (ω, μ, σ). Since the logarithm in Equation (9) contains a summation sign, the derivation process is difficult. Therefore, the Expectation-Maximization algorithm (EM) is introduced to improve it.

[0185] (2) EM algorithm

[0186] The EM algorithm includes the E step (expectation-step) and the M step (maximization-step), and is suitable for small sample parameter estimation problems.

[0187] 1) Step E:

[0188] In the sample set X=(x1,x2,…,x n ,…,x N ) introduces the hidden variable γ n,m , represents the sample x n It is sampled from the mth Gaussian component. Expand the sample to get the complete data set:

[0189] (x n ; γ n,1 ,γ n,2 ,…,γ n,M ) n∈[1,N] and n∈N * (10)

[0190] To determine: ① which Gaussian component generates the nth sample; ② if the sample is generated by the mth Gaussian component, the probability that the Gaussian component generates the nth sample, the likelihood function is introduced:

[0191]

[0192] Taking m=1 as an example, the derivation process is:

[0193]

[0194] The likelihood function for non-missing data can be expressed as:

[0195]

[0196] In order to maximize lnf X,Γ (x,γ;ω,μ,σ), select the Q function and maximize it:

[0197]

[0198] Among them, the estimate of γ E(γ n,m x n ;ω i ,μ i ,σ i ) can be further expressed as:

[0199]

[0200] 2) M step:

[0201] Based on the Q function, the model parameters for the next iteration are obtained with the goal of maximizing Q:

[0202] ω i+1 ,μ i+1 ,σ i+1 =argmaxQ(ω,μ,σ;ω i ,μ i ,σ i ) (16)

[0203] Let the first-order derivative of the Q function be zero, and we get:

[0204]

[0205] Where: ωi+1 、μ i+1 and σ i+1 are the weight, mean and covariance matrix of the m-th class sample at the i+1th iteration respectively.

[0206] Distribution network linearized power flow model:

[0207] Based on the linear power flow model, the AC power flow equation in the form of node injection power is:

[0208]

[0209] Where: i, j are node numbers; N is the number of nodes; U i 、U j are the voltage amplitudes of nodes i and j respectively; P i , Q i are the active power and reactive power injected at node i respectively; θ ij is the voltage phase angle difference between nodes i and j; G ij 、B ij is the element in the node admittance matrix.

[0210] The approximate assumption shown in formula (19) is adopted. This approximation has been proven to be good at approximating line power flows in two typical cases (high R / X ratio and low R / X ratio).

[0211] g ij U i (U i -U j cosθ ij )≈g ij U i (U i -U j )

[0212] =g ij (1+ΔU i )(ΔU i -ΔU j )

[0213] ≈g ij (ΔU i -ΔU j )

[0214] =g ij (U i -U j ) (19)

[0215] This approximation allows the voltage amplitude and phase angle to be decoupled, as shown in equation (2):

[0216]

[0217] Similarly, we can get:

[0218]

[0219] The line flow P can also be easily obtained from formula (2): ij The linear expression of:

[0220] P ij =g ij (U i -U j )-b ij (θ i -θ j ) (twenty two)

[0221] The matrix form of formula (2) and formula (2) is shown in formula (2):

[0222]

[0223] In formula (2), both θ and U are composed of three sub-vectors, corresponding to the Vθ node (balance node), PV node, and PQ node, respectively. Arranging these nodes in the order of Vθ, PV, and PQ yields:

[0224]

[0225]

[0226] Wherein, subscripts R, S, and L correspond to the Vθ node, PV node, and PQ node, respectively.

[0227] Arranging the node admittance matrix in the same way yields:

[0228]

[0229] According to the known parameters θ of Vθ node, PV node and PQ node R , U R and U S , transform formula (2) into the following form:

[0230]

[0231] in:

[0232]

[0233]

[0234]

[0235] U=U L (29)

[0236] Performing basic row transformation on equation (26) yields:

[0237]

[0238]

[0239] Combining the first part of Equation (30) and the second part of Equation (31) into one equation can achieve the decoupling of voltage amplitude and phase angle, as shown in Equation (32):

[0240]

[0241] in:

[0242] H=H-NL -1 M (33)

[0243] L=L-MH -1 N (34)

[0244] According to formula (32), the expressions of node voltage amplitude and phase angle are as follows:

[0245]

[0246] U=L -1 QL -1 MH -1 P (36)

[0247] Probabilistic power flow calculation method:

[0248] The linear invariance of the Gaussian mixture model shows that if the random variable X follows a Gaussian distribution and Y is a linear transformation of X, Y = C + AX, then Y also follows a Gaussian distribution after the linear transformation. Equation (36) indicates that the node voltage amplitude U is a linear function of the node injected active power P and the node injected reactive power Q. Therefore, to obtain a linear expression for the node voltage amplitude U with respect to the node injected active power P, the node injected reactive power Q needs to be processed. This chapter's model considers both the uncertainties of distributed PV and loads. Without considering the reactive power control of PV inverters, the distributed PV reactive power can be considered zero. In this case, the node-injected active power P is affected by both the distributed PV active output and the load active power, while the node-injected reactive power Q depends solely on the load reactive power. The node power factor angle varies significantly, making it impossible to express the node-injected reactive power Q as the tangent of the power factor angle multiplied by the node-injected active power P. Given that the R / X ratio within a distribution substation is relatively high, the node voltage in the substation is more affected by active power than reactive power, and the reactive power within the same substation varies little. Therefore, the node-injected reactive power Q can be approximated by the mean of the node load reactive power historical data. This yields a linear transformation U of the node-injected active power P. Since the node-injected active power P is modeled based on a Gaussian mixture model, after the linear transformation in the distribution network linearized power flow model, the node voltage U also follows the Gaussian mixture model. Similarly, the line power flow also follows the Gaussian mixture model.

[0249] In summary, the generalized equation shown in Equation (37) is used to describe the functional relationship between the node voltage and line power in the probabilistic power flow and the node injected active power:

[0250] Y=C+AX (37)

[0251] Where X represents the node injected active power; Y represents variables such as node voltage amplitude, phase angle, and line active power; C and A represent constant coefficient vectors and matrices, respectively.

[0252] Taking the node voltage amplitude as an example for derivation and verification, the node voltage amplitude obeys Gaussian distribution, and its mean phasor is Aμ m +C, the covariance matrix is ​​Aσ m A T , so the joint probability density function of the node voltage amplitude can be expressed as:

[0253]

[0254]

[0255] After multiple integration, the cumulative distribution function of the node voltage amplitude can be obtained:

[0256]

[0257] Where: Φ m (y) is N m The multiple integral of (y) is expressed as:

[0258]

[0259] Quantitative assessment of the impact of distributed photovoltaic access:

[0260] Utility Theory:

[0261] Existing research often uses a linear function to characterize severity, where severity is proportional to the magnitude of the voltage (or power flow) offset. However, this approach tends to underestimate the severity of high-risk events, and the resulting risk results often lack credibility. This section introduces utility theory from economics and uses a utility function to characterize severity. Utility functions are categorized into three types based on market participants' attitudes toward risk: conservative, adventurous, and neutral.

[0262] The utility function is recorded as E(W), which is a continuous function. W is the expected value of profit and loss. Its first-order derivative E'(W)>0, that is, E(W) is an increasing function of W. The second-order derivative of E(W) is E"(W):

[0263] (1) When E(W) < 0, E(W) is a convex function. At this time, the utility growth rate decreases with the increase of W, and the utility tends to saturate with the increase of W. This shows that compared with the pursuit of profit, market participants are more risk-averse and afraid of loss. Therefore, they have an averse attitude towards risk, which corresponds to a conservative utility function.

[0264] (2) When E(W) = 0, E(W) is a linear function, indicating that utility is linearly related to W and the growth rate of utility is constant, corresponding to a neutral utility function;

[0265] (3) When E(W)>0, E(W) is a concave function. At this time, the utility increases with the growth of W, and the growth rate also increases accordingly, indicating that market participants have a favorable attitude towards risk and expect to obtain greater profits, which corresponds to the adventurous utility function.

[0266] Quantitative assessment indicators of the impact of distributed photovoltaic access:

[0267] (1) Voltage over-limit risk indicator:

[0268] Excessive voltage in the distribution network can affect the insulation of power equipment. Reduced voltage in the distribution network can increase power and energy losses, and even affect the stability of the network's operation, causing system collapse and widespread power outages. Therefore, it is essential to incorporate voltage over-limit risk indicators into the indicator system.

[0269] To study the impact of distributed photovoltaic access, it is necessary to consider both the node voltage exceeding the lower limit due to excessive load and the node voltage exceeding the upper limit due to photovoltaic access. To reflect the difference between the two situations, the node voltage exceeding limit risk index is divided into the node voltage exceeding upper limit index Idx UO and node voltage exceeds lower limit indicator Idx UB The specific calculation formula of the indicator is as follows:

[0270]

[0271]

[0272] Where: K is the total sample size; s is the number of sampling times; Sev UO (U s,max ) and Sev UO (U s,min ) are the severity functions of the node voltage exceeding the upper limit and the lower limit, respectively, which are used to describe the severity of the node voltage exceeding the limit. Their definitions are shown in Equations (44) and (46):

[0273]

[0274]

[0275]

[0276]

[0277] Where: U s,i is the voltage amplitude of node i at the sth sampling time; U OV and U UV are the upper and lower limits of the node voltage respectively.

[0278] (2) Tidal current over-limit risk index:

[0279] When branch currents do not exceed the thermal stability limit, they have little impact on the probability of branch outage. If branch currents exceed the allowable range, the line's overcurrent and overload protection devices will operate. The duration of protection operation is inversely proportional to the extent of the current excursion. The greater the current excursion, the lower the probability of returning to within the allowable limit, and the greater the probability of line outage. Because line outages can cause load loss and thus affect economic efficiency, it is necessary to establish branch current excursion risk indicators in risk assessments of large-scale distributed photovoltaic distribution networks.

[0280] The calculation formula of the tidal current over-limit risk index is as follows:

[0281]

[0282] Where: Sev B (P s,max ) is the severity function of branch current exceeding the limit, which is used to describe the severity of branch current exceeding the limit. Its definition is shown in formula (49):

[0283]

[0284]

[0285] Where: P s,l is the active power flowing in line l at the sth sampling time; L is the total number of lines in the distribution area; P l,OV is the rated transmission power of line l.

[0286] (3) Node voltage deviation index:

[0287] The value of the node voltage deviation index can describe the distribution of node voltages in the distribution substation area. The smaller the node voltage deviation index is, the more concentrated the node voltage distribution in the distribution substation area is, and the better the power quality is.

[0288] The calculation formula for the node voltage deviation index is as follows:

[0289]

[0290] Where: is the average value of the node voltage in the distribution station area at the sth sampling time.

[0291] (4) Line loss index:

[0292] Since both load and distributed photovoltaic output are described using probabilistic models, traditional active power loss expressions are difficult to describe probabilistic power flow active power loss. The approximate active power loss expression for the system is given as follows:

[0293]

[0294] Where: N L is the total number of branches in the distribution area; R k is the resistance of the branch k connecting node i and node j.

[0295] Quantitative assessment process of the impact of distributed photovoltaic access:

[0296] In summary, the proposed quantitative assessment process for the impact of distributed photovoltaic access is as follows:

[0297] Step 1: Input the raw data required for the assessment, including distribution station area system parameters, historical load data, historical solar irradiation intensity data, and the distributed photovoltaic access scheme to be assessed;

[0298] Step 2: Calculate the historical data of node injection power based on the historical data of solar irradiation intensity, the location and capacity of distributed photovoltaic access;

[0299] Step 3: Form a Gaussian mixture model of node injection power based on the historical data of node injection power;

[0300] Step 4: Perform probabilistic power flow calculation to obtain the probability distribution function of node voltage and branch power flow;

[0301] Step 5: Generate K samples according to the distribution function;

[0302] Step 6: Calculate the quantitative evaluation index value of the distribution network power flow over-limit risk.

[0303] Based on the above quantitative assessment results of the distribution network power flow over-limit risk, the PV load capacity margin of any node in the distribution network can be calculated. The calculation process is as follows:

[0304] Step 1: Based on the Gaussian mixture model, multiple simulations are performed on the operation of the distribution network. The risk probability and severity faced by each node in the distribution network can be obtained by calculating the above indicators.

[0305] Step 2: Select a certain risk probability. Assuming that there is a 95% probability that each node in the distribution network can operate within the normal indicator range, it can be determined that the distribution network can operate safely and stably at this time.

[0306] Step 3: On this basis, the photovoltaic grid-connected capacity of node n in the distribution network can be increased for further simulation. When the simulation results show that the probability of each indicator is close to the edge of its normal value with 95%, it is determined that the photovoltaic carrying capacity of node n in the distribution network has reached its limit. Subtract the photovoltaic capacity before the increase This is the photovoltaic load capacity margin of the node:

[0307] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

[0308] Many other changes and modifications can be made without departing from the spirit and scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for quantitative assessment and risk control of the impact of distributed photovoltaic access, characterized in that: The method comprises: Based on the historical data of load power at distribution network nodes, historical data of solar irradiation intensity, and the photovoltaic installation status or access plan of the distribution network, a Gaussian mixture model of node injection power is constructed; A linearized power flow model for the distribution network is constructed. The uncertainty of node injection power is determined based on a Gaussian mixture model. The probability density function of node voltage amplitude and branch active power is obtained through probabilistic power flow calculation to quantitatively assess the impact of distributed photovoltaic access. Based on the quantitative assessment results of the impact of distributed photovoltaic access, the photovoltaic load capacity margin of any node in the distribution network is calculated to obtain the maximum photovoltaic grid-connected capacity of any node in the distribution network under the risk probability; Conduct a quantitative assessment of the impact of distributed photovoltaic access, specifically including: using utility theory and quantitative assessment indicators of the impact of distributed photovoltaic access: Utility Theory: Based on the utility theory in economics, the utility function is used to characterize the severity. The utility function is divided into three categories according to the attitude of market participants towards risk: conservative, adventurous, and neutral. The utility function is recorded as E(W), which is a continuous function. W is the expected value of profit and loss. Its first-order derivative E'(W)>0, that is, E(W) is an increasing function of W. The second-order derivative of E(W) is E"(W): (1) When E(W) < 0, E(W) is a convex function. At this time, the utility growth rate decreases with the increase of W, and the utility tends to saturation with the increase of W, which corresponds to a conservative utility function. (2) When E(W) = 0, E(W) is a linear function, indicating that utility is linearly related to W and the growth rate of utility is constant, corresponding to a neutral utility function; (3) When E(W)>0, E(W) is a concave function. At this time, the utility increases with the growth of W, and the growth rate also increases accordingly, which corresponds to the risk-taking utility function. Quantitative assessment indicators of the impact of distributed photovoltaic access: (1) Voltage over-limit risk indicator: The node voltage over-limit risk index is divided into the node voltage over-limit index Idx UO and node voltage exceeds lower limit indicator Idx UB The specific calculation formula of the indicator is as follows: In the formula: K is the total sample size; s is the number of sampling times; Sev UO (U s,max ) and Sev UB (U s,min ) are the severity functions of the node voltage exceeding the upper limit and the lower limit, respectively, which are used to describe the severity of the node voltage exceeding the limit. Their definitions are shown in Equations (44) and (46): Where: U s,i is the voltage amplitude of node i at the sth sampling time, U OV and U UV are the upper and lower limits of the node voltage respectively; (2) Tidal current over-limit risk index: Establishing branch power flow over-limit risk indicators in risk assessment of distribution networks containing large-scale distributed photovoltaics; The calculation formula of the tidal current over-limit risk index is as follows: Where: Sev B (P s,max ) is the severity function of branch current exceeding the limit, which is used to describe the severity of branch current exceeding the limit. Its definition is shown in formula (49): Where: P s,l is the active power flowing in line l at the sth sampling time; P l,OV is the rated transmission power of line l, L is the total number of lines in the distribution area; (3) Node voltage deviation index: The value of the node voltage deviation index can describe the distribution of node voltages in the distribution substation area. The smaller the node voltage deviation index, the more concentrated the node voltage distribution in the distribution substation area, and the better the power quality. The calculation formula for the node voltage deviation index is as follows: Where: is the average value of the node voltage in the distribution area at the sth sampling time; (4) Line loss index: The approximate active power loss expression of the system is given as follows: Where: N L is the total number of branches in the distribution area; R k is the resistance of the branch connecting node i and node j; The calculation of the photovoltaic load capacity margin of any node in the distribution network includes: Step 1: Based on the Gaussian mixture model, multiple simulations are performed on the operation of the distribution network, and the risk probability and severity faced by each node in the distribution network are obtained according to the calculation of indicators; Step 2: Select the risk probability and determine that when there is a 95% probability that each node in the distribution network can maintain operation within the normal indicator range, it is determined that the distribution network can operate safely and stably at this time; Step 3: Increase the photovoltaic grid-connected capacity of node n in the distribution network for further simulation. When the simulation results show that when the various indicators are close to the edge of their normal operating values ​​with a probability of 95%, it is determined that the photovoltaic carrying capacity of node n in the distribution network has reached its limit. The increased photovoltaic capacity Subtract the photovoltaic capacity before the increase This is the photovoltaic load capacity margin of the node:

2. A method for quantitative assessment and risk control of impacts of distributed photovoltaic access according to claim 1, characterized in that: According to the historical data of distribution network node load power, historical data of solar radiation intensity and the photovoltaic installation situation or access plan of the distribution network, the historical data of node injection power is calculated, and a Gaussian mixture model of node injection power is constructed using the historical data of node injection power.

3. The method for quantitative assessment and risk control of distributed photovoltaic access impact according to claim 2, characterized in that: The uncertainty of distributed photovoltaic power generation is characterized, and it is determined that the distributed photovoltaic output of the same distribution area follows the same distribution. For a given distributed photovoltaic access scheme, that is, the distributed photovoltaic access location and capacity are both known, the distributed photovoltaic output corresponding to each node can be obtained according to formula (1): Where: η is the conversion efficiency of the photovoltaic inverter; P PV,i is the distributed photovoltaic installation capacity at node i; P in,i (t)=P PV,i (t)-P load,i (t) (2) Where: P in,i (t) is the injected power at node i at time t; P load,i (t) is the load power at node i at time t; Based on the one-year statistical data of node load and light irradiation intensity in the distribution station area, a statistical analysis is performed on the node load data and light irradiation intensity data within each hour. The data of the injected power of each node within each hour is generated, and the PDF of the joint injected power of the nodes in the corresponding period is obtained, that is, the historical data of the node injected power is obtained.

4. The method for quantitative assessment and risk control of distributed photovoltaic access impact according to claim 1, characterized in that: The constructing of the Gaussian mixture model of the node injection power includes: The random variable that determines the node injection power is X, and its probability distribution is represented by the superposition of several Gaussian distributions: Where: f X (x) is the joint probability density function of the random variable X; ω m is the weight coefficient; W is the dimension of X; N m Represents a multidimensional normal distribution, which is called the mth Gaussian component of the Gaussian mixture model GMM; det is the determinant of the matrix; M is the total number of Gaussian components; μ m and σ m are the mean vector and covariance matrix of the mth Gaussian component respectively; In order to solve the Gaussian mixture model shown in equation (3), it is necessary to further determine the unknown parameters ω of each Gaussian component: m 、μ m and σ m , so that the Gaussian mixture model is closest to the actual sample obtained, and the parameters to be determined can be obtained by the maximum likelihood estimation method.

5. The method for quantitative assessment and risk control of distributed photovoltaic access impact according to claim 4, characterized in that: Through probabilistic power flow calculation, specifically including: The generalized equation shown in Equation (37) is used to describe the functional relationship between the node voltage and line power and the node injected active power in the probabilistic power flow: Y=C+AX (37) Where: X represents the node injected active power; Y represents the variables such as node voltage amplitude, phase angle and line active power; C and A represent the constant coefficient vector and matrix respectively; Taking the node voltage amplitude as an example for derivation and verification, the node voltage amplitude obeys Gaussian distribution, and its mean phasor is Aμ m +C, the covariance matrix is ​​Aσ m A T , so the joint probability density function of the node voltage amplitude can be expressed as: After multiple integration, the cumulative distribution function of the node voltage amplitude can be obtained: Where: Φ m (y) is N m The multiple integral of (y) is expressed as:

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