A probabilistic prediction method for grid static voltage stability margin considering uncertainty of renewable energy

Abstract

The present invention relates to a method for predicting the probability of a static voltage stability margin of a power grid considering the uncertainty of new energy sources, specifically comprising: constructing a power prediction error model of new energy sources represented by wind power and photovoltaics; constructing a static scene generation model of wind power and photovoltaics based on the prediction error model and Monte Carlo sampling; constructing a single-scene static voltage stability margin prediction method based on deep learning; and using a kernel density estimation method to generate a probability prediction result of a static voltage stability margin of a power grid considering the uncertainty of new energy sources. The present invention has the following advantages: on the one hand, the proposed scene generation model based on the prediction error of new energy sources considers the randomness of new energy power generation, and the obtained static voltage stability margin probability distribution can provide more reference information for dispatchers; on the other hand, a deep learning model is used to predict the static voltage stability margin of each scene, while ensuring the accuracy and efficiency of probability prediction, and is suitable for online applications.

Description

Technical Field

[0001] The present invention relates to the research field of power system safety and stability analysis, and in particular to a method for predicting the probability of static voltage stability margin of a power grid taking into account the uncertainty of new energy sources. Background Art

[0002] In recent years, many major power outages have occurred around the world, and power grid safety has once again become the focus of attention from all parties. For the growing number of power outages, there are direct causes such as natural disasters and accidents, as well as deep-seated causes such as frequency instability and voltage instability. Relevant studies have shown that compared with the synchronous operation stability and power angle stability of the power system, voltage stability is more sudden and hidden, and power outages caused by voltage instability account for a large proportion. Among them, with the development of the power system, the phenomenon of long and medium lines, heavy loads and insufficient reactive power reserves in the power grid has become increasingly prominent, and the static voltage stability margin of the system has become smaller and smaller. In addition, the randomness of the power generation power of new energy has led to a stronger uncertainty in the static voltage stability margin, which has increased the possibility of power outages caused by static voltage stability instability. Therefore, predicting the static voltage stability margin of a power system containing a large number of new energy sources is of great significance for the safe and stable operation of the power grid.

[0003] The existing studies on the probability analysis of static voltage stability margin mainly include analytical method, approximate method and Monte Carlo simulation method. The analytical method represented by the semi-invariant method requires linearization of the input-output relationship, which has a large error when the power fluctuation is large. The existing point estimation method and Monte Carlo simulation method both require multiple continuous power flow calculations, which are difficult to meet the requirements of online prediction. Summary of the invention

[0004] The present invention aims to overcome the defects of the above-mentioned static voltage stability margin probability prediction and provide a method for predicting the static voltage stability margin probability of a power grid taking into account the uncertainty of new energy. To achieve the above-mentioned goal, the present invention adopts the following technical solutions:

[0005] Based on the power prediction error model of new energy represented by wind power and photovoltaics, and the static scene generation model of wind power and photovoltaics constructed based on the power prediction error model and Monte Carlo sampling, the prediction method is to build a deep neural network and conduct offline training, and predict the static voltage stability margin of the power grid online based on the trained deep neural network, including:

[0006] Step 1: Randomly generate a large number of initial operating states and use the continuous power flow method to calculate the static voltage stability margin K of each operating state. p , and establish a sample database (X, K p ), the deep neural network is trained offline based on the sample database, where the continuous power flow equation is as follows:

[0007]

[0008] Among them, P G Indicates the active power of the generator; P G0 Indicates the initial active power of the generator; P Gd Indicates the growth direction of the generator active power; P L , Q L Indicates the active and reactive power of the load; P L0 , Q L0 Indicates the initial active and reactive power of the load; P Ld , Q Ld Indicates the growth direction of active and reactive power of the load. The condition for the end of training is that the loss function is minimized. The trained model is a black box.

[0009] Step 2: During online prediction, the network power flow is calculated based on the network topology and source-load prediction data, and the node voltage amplitude V and phase angle θ are obtained as online input X. The trained deep neural network is used to predict the grid static voltage stability margin K. p .

[0010] In the above-mentioned probabilistic prediction method of the static voltage stability margin of the power grid considering the uncertainty of new energy, a power prediction error model of new energy represented by wind power and photovoltaics is constructed, specifically including: based on the historical predicted power and actual power data of wind power and photovoltaics, a distribution model is used to fit the statistical distribution results of the prediction error, and a probability density function (PDF) and cumulative distribution function (CDF) that can characterize the distribution of the new energy power prediction error are obtained.

[0011] In the above-mentioned method for predicting the static voltage stability margin probability of power grid considering the uncertainty of new energy, the prediction errors of wind power and photovoltaic power have the distribution characteristics of peak and thick tail, so the generalized error distribution is used to fit their distribution. The specific model is as follows:

[0012] The probability density function of the generalized error distribution is:

[0013]

[0014] The cumulative distribution function of the generalized error distribution is:

[0015]

[0016] Among them, Δp represents the per-unit value of wind power and photovoltaic power prediction error; α and β are shape fitting parameters; μ is the position fitting parameter.

[0017] In the above-mentioned method for predicting the static voltage stability margin probability of a power grid considering the uncertainty of new energy, a wind power and photovoltaic static scene generation model based on the prediction error model and Monte Carlo sampling is constructed, which specifically includes: using the Latin hypercube sampling method to perform uniform Monte Carlo sampling on the cumulative distribution function of the prediction error, and using Cholesky decomposition to rearrange the scenes of each new energy station. The specific steps are as follows:

[0018] Step 1: Sampling the forecast error cumulative distribution function

[0019] Assume Δp1,…Δp N are N independent wind power and photovoltaic power prediction error random variables, where the nth random variable Δp n CDFF n (Δp n ) and its inverse function Exists as follows:

[0020] Y n =F n (Δp n ), (n=1,2...,N)

[0021]

[0022] For each random variable Δp n By sampling in M ​​equal parts, an N×M matrix ΔP can be generated:

[0023]

[0024] Step 2: Rearrange using Cholesky decomposition

[0025] Step 2.1: Randomly generate an N×M matrix L, where the nth row vector of the matrix L is randomly generated by 1, 2, …, M, representing the position where the nth row vector in the ΔP matrix should be arranged;

[0026] Step 2.2: Calculate the correlation coefficient ρ between the rows of matrix L L ρ L Is a positive definite symmetric positive definite matrix, which is decomposed into a non-singular lower triangular matrix D by Cholesky decomposition:

[0027] ρ L =DD T

[0028] Step 2.3: Calculate the N×M matrix G according to the following formula:

[0029] G=D -1 L

[0030] Step 2.4: The elements of each row in the matrix L are replaced according to the order of the element sizes of the corresponding row in the matrix G;

[0031] Step 2.5: The elements of each row in the matrix ΔP are rearranged according to the arrangement of the elements of the corresponding row in the updated matrix L;

[0032] The actual wind power and photovoltaic output scenarios are:

[0033]

[0034] Among them, P Wind,i , P PV,i are the active power output scenarios of the i-th wind farm and photovoltaic power station respectively; P Wind_f,i , P PV_f,i are the predicted active power values ​​of the wind farm and photovoltaic power station at that moment; ΔP Wind,i , ΔP PV,i are the active power prediction error sampling values ​​of the i-th wind farm and photovoltaic power station respectively.

[0035] In the above-mentioned method for predicting the probability of the static voltage stability margin of a power grid considering the uncertainty of new energy, a kernel density estimation method is also used to generate a probability prediction result of the static voltage stability margin of a power grid considering the uncertainty of new energy. Specifically, based on the deterministic prediction results of the static voltage stability margin of multiple scenarios, the kernel density estimation method is used to smoothly fit the margin probability distribution. The kernel density estimation peak function is as follows:

[0036]

[0037] Where h is the bandwidth; x i is the stability margin sample point to be fitted; K(·) is the kernel function, Xi is the predicted result Kp, which is used to estimate the distribution probability of Xi and perform smooth fitting on the distribution probability.

[0038] The present invention has the following technical effects: the present invention provides a method for predicting the probability of static voltage stability margin of a power grid taking into account the uncertainty of new energy sources, adopts generalized error distribution to realize modeling of wind power and photovoltaic power prediction error distribution, and samples the new energy prediction error based on Latin hypercube sampling, generates wind power and photovoltaic active output scenarios based on the sampling results, further adopts a deep neural network to construct a mapping relationship between network input and static voltage stability margin, realizes online prediction of static voltage stability margin, and finally uses kernel density estimation to obtain the probability prediction result of system static voltage stability margin. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The figure is a flow chart of the method of the present invention.

[0040] Figure 2 A wind power prediction error fitting effect diagram provided by an embodiment of the present invention.

[0041] Figure 3 A photovoltaic power prediction error fitting effect diagram provided by an embodiment of the present invention.

[0042] Figure 4 A sampling schematic diagram based on the Latin hypercube method provided in an embodiment of the present invention.

[0043] Figure 5 A deep neural network topology diagram provided in an embodiment of the present invention.

[0044] Figure 6 A static voltage stability margin probability distribution diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] like Figure 1 As shown, the present invention provides a method for predicting the probability of static voltage stability margin of a power grid considering the uncertainty of new energy sources, which specifically includes:

[0047] Construct a power prediction error model for new energy sources represented by wind power and photovoltaics;

[0048] Construct a static scenario generation model for wind power and photovoltaic power based on prediction error model and Monte Carlo sampling;

[0049] Construct a single-scenario static voltage stability margin prediction method based on deep learning;

[0050] The kernel density estimation method is used to generate the probability prediction results of the static voltage stability margin of the power grid considering the uncertainty of renewable energy.

[0051] Preferably, the power prediction error model of new energy represented by wind power and photovoltaics is constructed, specifically including fitting the statistical distribution results of the prediction error based on the historical predicted power and actual power data of wind power and photovoltaics using a suitable distribution model to obtain a probability density function (PDF) and cumulative distribution function (CDF) that can characterize the distribution of the new energy power prediction error.

[0052] In particular, the forecast error model for new energy power represented by wind power and photovoltaic power takes into account that the forecast errors of wind power and photovoltaic power have peak and thick tail distribution characteristics, so the generalized error distribution is used to fit their distribution. The specific model is as follows:

[0053] The probability density function of the generalized error distribution is:

[0054]

[0055] The cumulative distribution function of the generalized error distribution is:

[0056]

[0057] Among them, Δp represents the per-unit value of wind power and photovoltaic power prediction error; α and β are shape fitting parameters; μ is the position fitting parameter.

[0058] In particular, the wind power forecast error fitting effect is as follows Figure 2 As shown in the figure, the photovoltaic power prediction error fitting effect is as follows Figure 3 shown.

[0059] Preferably, the wind power and photovoltaic static scene generation model based on the prediction error model and Monte Carlo sampling is constructed, specifically comprising: using Latin hypercube sampling method to perform uniform Monte Carlo sampling on the prediction error cumulative distribution function, and using Cholesky decomposition to rearrange each new energy site scene, the specific steps are:

[0060] Step 1: Sampling the forecast error cumulative distribution function

[0061] Assume Δp1,…Δp N are N independent wind power and photovoltaic power prediction error random variables, where the nth random variable Δp n CDFF n (Δp n ) and its inverse function Exists as follows:

[0062] Y n =F n (Δp n ), (n=1,2...,N)

[0063]

[0064] For each random variable Δp n By sampling in M ​​equal parts, an N×M matrix ΔP can be generated:

[0065]

[0066] Step 2: Rearrange using Cholesky decomposition

[0067] Step 2.1: Randomly generate an N×M matrix L, where the nth row vector of the matrix L is randomly generated by 1, 2, …, M, representing the position where the nth row vector in the ΔP matrix should be arranged.

[0068] Step 2.2: Calculate the correlation coefficient ρ between the rows of matrix L L ρ L Is a positive definite symmetric positive definite matrix, which is decomposed into a non-singular lower triangular matrix D by Cholesky decomposition:

[0069] ρ L =DD T

[0070] Step 2.3: Calculate the N×M matrix G according to the following formula:

[0071] G=D -1 L

[0072] Step 2.4: The elements of each row in the matrix L are replaced according to the order of the element sizes of the corresponding row in the matrix G.

[0073] Step 2.5: The elements of each row in the matrix ΔP are rearranged according to the element arrangement of the corresponding row of the updated matrix L.

[0074] The actual wind power and photovoltaic output scenarios are:

[0075]

[0076] Among them, P Wind,i , P PV,i are the active power output scenarios of the i-th wind farm and photovoltaic power station respectively; P Wind_f,i , P PV_f,i are the predicted active power values ​​of the wind farm and photovoltaic power station at that moment; ΔP Wind,i , ΔP PV,i are the active power prediction error sampling values ​​of the i-th wind farm and photovoltaic power station respectively.

[0077] In particular, the Latin hypercube sampling method is used to perform uniform Monte Carlo sampling on the prediction error cumulative distribution function. The sampling function is as follows. The specific operation is as follows: Figure 4 shown.

[0078] Δp=F -1 (Y)

[0079] Where Δp represents the per-unit value of wind power and photovoltaic power prediction error; F -1(·) represents the inverse function of the cumulative distribution function of the new energy error distribution; Y represents the cumulative distribution probability value, and its value range is [0,1].

[0080] Preferably, the single-scenario static voltage stability margin prediction method based on deep learning is constructed, specifically comprising constructing a deep neural network and performing offline training, and online predicting the static voltage stability margin of the power grid based on the trained deep neural network.

[0081] In particular, the construction of a deep neural network and offline training specifically includes building a multi-hidden layer neural network. The network structure of the embodiment of the present invention is as follows: Figure 5 As shown, a large number of initial operating states are randomly generated, and the static voltage stability margin K of each operating state is calculated using the continuous power flow method. p , and establish a sample database (X, K p ), offline training of deep neural network based on sample database.

[0082] The continuous power flow equation is as follows:

[0083]

[0084] Among them, P G Indicates the active power of the generator; P G0 Indicates the initial active power of the generator; P Gd Indicates the growth direction of the generator active power; P L , Q L Indicates the active and reactive power of the load; P L0 , Q L0 Indicates the initial active and reactive power of the load; P Ld , Q Ld Indicates the growth direction of load active and reactive power.

[0085] In particular, the online prediction of the static voltage stability margin of the power grid based on the trained deep neural network specifically includes performing power flow calculation on the network based on the network topology and source-load prediction data, obtaining the node voltage amplitude V and phase angle θ as online input X, and using the trained deep neural network to predict the static voltage stability margin K of the power grid. p .

[0086] As a preference, Figure 6 As shown, the kernel density estimation method is used to generate the probability prediction result of the static voltage stability margin of the power grid considering the uncertainty of new energy, specifically including the deterministic prediction result of the static voltage stability margin based on multiple scenarios, and the kernel density estimation method is used to smooth the margin probability distribution. The kernel density estimation peak function is as follows:

[0087]

[0088] Where h is the bandwidth; x i is the stability margin sample point to be fitted; K(·) is the kernel function.

[0089] The above-described method for predicting the probability of static voltage stability margin of power grid considering the uncertainty of new energy has the following beneficial effects: generalized error distribution is used to realize modeling of wind power and photovoltaic power prediction error distribution, and new energy prediction error is sampled based on Latin hypercube sampling, wind power and photovoltaic active output scenarios are generated based on the sampling results, and a deep neural network is further used to construct a mapping relationship between network input and static voltage stability margin to realize online prediction of static voltage stability margin, and finally kernel density estimation is used to obtain the probability prediction result of system static voltage stability margin, which can provide important reference for the formulation and implementation of static voltage stability prevention and control measures.

[0090] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0091] It should be understood that the above description of the preferred embodiment is relatively detailed and cannot be regarded as limiting the scope of protection of the present invention. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, all of which fall within the scope of protection of the present invention. The scope of protection requested for the present invention shall be based on the attached claims.

Claims

1. A method for predicting the probability of static voltage stability margin of a power grid considering the uncertainty of new energy sources, characterized in that: Based on the power prediction error model of new energy represented by wind power and photovoltaics, and the static scene generation model of wind power and photovoltaics constructed based on the power prediction error model and Monte Carlo sampling, the prediction method is to build a deep neural network and conduct offline training, and predict the static voltage stability margin of the power grid online based on the trained deep neural network, including: Step 1: Randomly generate a large number of initial operating states and use the continuous power flow method to calculate the static voltage stability margin K of each operating state. p , and establish a sample database (X, K p ), the deep neural network is trained offline based on the sample database, where the continuous power flow equation is as follows: Among them, P G Indicates the active power of the generator; P G0 Indicates the initial active power of the generator; P Gd Indicates the growth direction of the generator active power; P L , Q L Indicates the active and reactive power of the load; P L0 , Q L0 Indicates the initial active and reactive power of the load; P Ld , Q Ld Indicates the growth direction of active and reactive power of the load. The condition for the end of training is that the loss function is minimized. The trained model is a black box. Step 2: During online prediction, the network power flow is calculated based on the network topology and source-load prediction data, and the node voltage amplitude V and phase angle θ are obtained as online input X. The trained deep neural network is used to predict the grid static voltage stability margin K. p ; Construct a power forecast error model for new energy represented by wind power and photovoltaics, specifically including: based on the historical forecast power and actual power data of wind power and photovoltaics, use the distribution model to fit the statistical distribution results of the forecast error, and obtain the probability density function PDF and cumulative distribution function CDF that can characterize the distribution of the new energy power forecast error; The prediction errors of wind power and photovoltaic power both have peak and thick tail distribution characteristics, so the generalized error distribution is used to fit their distribution. The specific model is as follows: The probability density function of the generalized error distribution is: The cumulative distribution function of the generalized error distribution is: Among them, Δp represents the per-unit value of wind power and photovoltaic power prediction error; α and β are shape fitting parameters; μ is the position fitting parameter; A wind power and photovoltaic static scene generation model based on the prediction error model and Monte Carlo sampling is constructed, which specifically includes: using the Latin hypercube sampling method to perform uniform Monte Carlo sampling on the prediction error cumulative distribution function, and using Cholesky decomposition to rearrange the scenes of each new energy station. The specific steps are as follows: Step 1: Sampling the forecast error cumulative distribution function Assume Δp1,…Δp N are N independent wind power and photovoltaic power prediction error random variables, where the nth random variable Δp n CDFF n (Δp n ) and its inverse function Exists as follows: Y n =F n (Δp n ), (n=1,2...,N) For each random variable Δp n By sampling in M ​​equal parts, an N×M matrix ΔP can be generated: Step 2: Rearrange using Cholesky decomposition Step 2.1: Randomly generate an N×M matrix L, where the nth row vector of the matrix L is randomly generated by 1, 2, …, M, representing the position where the nth row vector in the ΔP matrix should be arranged; Step 2.2: Calculate the correlation coefficient ρ between the rows of matrix L L ρ L Is a positive definite symmetric matrix, which is decomposed into a non-singular lower triangular matrix D by Cholesky decomposition: r L =DD T Step 2.3: Calculate the N×M matrix G according to the following formula: G=D -1 L Step 2.4: The elements of each row in the matrix L are replaced according to the order of the element sizes of the corresponding row in the matrix G; Step 2.5: The elements of each row in the matrix ΔP are rearranged according to the arrangement of the elements of the corresponding row in the updated matrix L; The actual wind power and photovoltaic output scenarios are: Among them, P Wind,i , P PV,i are the active power output scenarios of the i-th wind farm and photovoltaic power station respectively; P Wind_f,i , P PV_f,i are the predicted active power values ​​of the wind farm and photovoltaic power station at the current moment; ΔP Wind,i , ΔP PV,i are the active power prediction error sampling values ​​of the i-th wind farm and photovoltaic power station respectively; It also includes the use of kernel density estimation method to generate the probability prediction results of the static voltage stability margin of the power grid considering the uncertainty of new energy. Specifically, based on the deterministic prediction results of the static voltage stability margin of multiple scenarios, the kernel density estimation method is used to smooth the margin probability distribution. The kernel density estimation peak function is as follows: Where h is the bandwidth; x i is the stability margin sample point to be fitted; K(·) is the kernel function.

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