Data-driven linear state estimation method based on deep neural network

Abstract

The invention discloses a data-driven linear state estimation method based on a deep neural network. The method comprises the following steps: firstly, performing linear state estimation on a power distribution network in a complex field, and training to generate an error correction model based on historical measurement data and a state estimation result; and then, connecting the linear state estimation part with the error correction model in series, and correcting an error of a linear state estimation result by using a data driving method. According to the algorithm provided by the invention, the state quantity of the power distribution network can be accurately and efficiently solved in the three-phase unbalanced power distribution network under high-proportion new energy permeation, and technical support is provided for acquiring power distribution network information in real time.

Description

Technical Field

[0001] The present invention proposes a data-driven linear state estimation method based on a deep neural network, which belongs to the field of distribution networks. Background Art

[0002] With the global energy transformation, the penetration rate of distributed photovoltaic power generation in the distribution network has increased significantly. The access of a high proportion of new energy has changed the operating characteristics of the distribution network, bringing challenges to power balance, voltage stability and power quality. Photovoltaic power generation is volatile and random, and is greatly affected by factors such as weather and seasons, which greatly increases the complexity of distribution network state estimation. In real-time monitoring of distribution networks, state estimation is a key technology to provide reliable state information, which can be used for system optimization and fault diagnosis. However, traditional state estimation methods have limitations in dealing with the volatility of distributed photovoltaic power generation, especially in continuous time sections. The rapid changes in photovoltaic power will lead to large estimation errors, affecting the efficiency and safety of system operation.

[0003] Existing research on state estimation of high-penetration photovoltaic distribution networks mainly focuses on photovoltaic node modeling and robust algorithm exploration, which can be specifically divided into two categories: physical model methods and data-driven methods. State estimation based on physical models generally writes the measurement equations described by the physical model, and then calculates the state quantities from known quantity measurements (such as power, current, etc.) through existing methods. Similarly, the existing power system state estimation method based on the deep neural network (DNN) model selects known quantity measurements as the input features of the training data, the state quantity as the expected output, and solves the state quantity through data-driven fitting methods. The physical model method is based on the physical characteristics of the distribution network modeling, with good interpretability, but it is difficult to balance the calculation accuracy and efficiency. The data-driven method can solve the above problems, but lacks interpretability in most cases. Summary of the invention

[0004] Purpose of the invention: To solve the above problems, the present invention provides a data-driven linear state estimation method based on deep neural network, which can accurately obtain real-time state information in a photovoltaic distribution network with a high proportion. In addition, the present invention proposes a data-driven error correction model based on deep neural network, which combines the data-driven model with the real-time physical model state estimation, and can not only perform fast linear state estimation of the distribution network, but also use data-driven methods to correct linearization errors to ensure estimation accuracy.

[0005] Technical solution, in order to achieve the above-mentioned invention object, the present invention proposes a data-driven linear state estimation method based on a deep neural network, the method comprising the following steps:

[0006] Step 1: construct a basic information set required for data input according to parameter information of a three-phase unbalanced distribution network;

[0007] Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic distribution network to be tested, including node injection power, branch power, and photovoltaic power. Use the above historical data to perform state estimation on the distribution network to be tested using linear estimation method and nonlinear estimation method, respectively, to obtain linear estimation results and nonlinear estimation results;

[0008] Step 3: Generate sample data based on the above results: take the node injection power, branch power, and photovoltaic power as input, take the difference between the linear estimation result and the nonlinear estimation result, i.e., the linearization error, as output, train the deep learning model offline, and obtain a deep learning model that can predict the real-time linearization error;

[0009] Step 4: Utilize the real-time system characteristics and the complex domain linear state estimation method to calculate the initial linear estimation result, input the real-time system characteristics into the deep learning model trained in step 3, predict the linearization error, and finally superimpose the error onto the initial linear state estimation result to obtain the corrected linear state estimation result;

[0010] Step 5: After the calculation of the current time section is completed, jump to the next time section and repeat step 4 until all time sections are calculated.

[0011] Furthermore, the basic information set required for data input is constructed according to the parameter information of the three-phase unbalanced distribution network as described in step 1, and the parameter information includes the resistance and reactance of the three-phase branches of the distribution network, the equivalent resistance and reactance of the power supply model, and the equivalent resistance and reactance of the transformer, wherein the resistance and reactance of the three-phase branches of the distribution network are electrical parameters of each three-phase branch, which are used to describe the loss characteristics of electric energy during transmission; the equivalent resistance and reactance of the power supply model are used to characterize the characteristics of the power supply network; the equivalent resistance and reactance of the transformer are used to describe the performance and influence of the transformer; the node admittance matrix of the system to be tested is calculated and generated according to the above parameters;

[0012] Furthermore, in step 2, the linear estimation method and the nonlinear estimation method are used to estimate the state of the distribution network to be tested. The specific methods are as follows:

[0013] (1.1) Nonlinear state estimation

[0014] The nonlinear state estimation method is performed in the polar coordinate system, and the state variables are the voltage amplitude and voltage phase angle as shown below:

[0015]

[0016] Where x represents the state vector, Represents the kth node Phase voltage amplitude, Represents the kth node Phase voltage angle (k = 1, 2, ..., n), n is the number of system nodes;

[0017] The expression form of the measurement equation is z=h(x)+e, where z represents the measurement vector, h(·) represents the measurement function, and e represents the measurement residual vector. The specific measurement equation should be as follows:

[0018]

[0019]

[0020] In the formula, and The i-th node is Phase injected active power measurement and reactive power measurement, and They are the branches from node i to node j. Phase branch active power measurement and reactive power measurement, and They are respectively the admittance matrices The real and imaginary parts of the elements between phase and ψ, Represents the i-th node Phase voltage amplitude, represents the voltage amplitude of the ψ phase at the i-th node, represents the voltage amplitude of the jth node ψ phase, is the i-th node The phase angle difference between the phase and the j-th node ψ;

[0021] The weighted least squares method is used for state estimation. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). By iterative solution, the state quantity that minimizes the objective function is obtained. The vector form of the objective function is as follows:

[0022] minJ=[zh(x)] T R -1 [zh(x)]

[0023] Among them, J is the objective function, R is the standard deviation of the measurement noise, and its reciprocal is taken as the weight value;

[0024] Taking the partial derivative of the above formula with respect to x and setting it to zero, we get:

[0025] H(x)R -1 [zh(x)]=0

[0026] Among them, H(x) is the Jacobian matrix of the measurement function, and the specific expression is:

[0027]

[0028] Using Taylor series, the nonlinear measurement function is converted to (0) Expand at x (0) is the selected system initial value, and the following formula is used for iterative solution:

[0029] x (p+1) =x (p) +[H T (x (p) )R -1 H(x (p) )] -1 H T (x (p) )R -1 [zh(x (p) )]

[0030] where x (p) and x (p+1) are the state quantities obtained by solving the pth and p+1th iterations respectively;

[0031] The iteration stops when convergence occurs, that is, x (p+1) -x (p) The difference between (p+1) That is, the state quantity required to minimize the objective function The final solution obtained by this method is the nonlinear state estimate x N ;

[0032] (1.2) Linear state estimation

[0033] The linear state estimation is performed in the complex domain, and the state variables are complex values ​​of voltage, as follows:

[0034]

[0035] in, is the kth node The complex value of the phase voltage is expressed as Represents complex values The real part of Represents complex values The imaginary part of

[0036] For the linear state estimation in the complex domain, the node injection power measurement and branch power measurement are both in complex form and the calculation is completed in the complex domain;

[0037] Complex power measurement of the branch from node i to node j It is expressed as follows:

[0038]

[0039] Among them, P ij represents the active power measurement of the branch from node i to node j, Q ij represents the reactive power measurement of the branch from node i to node j, represents the complex value of the voltage at the ith node, represents the complex value of the current in the branch from node i to node j, and the superscript * indicates that the conjugate is taken;

[0040] According to the definition of the admittance matrix, the branch current It can be obtained by the following formula:

[0041]

[0042] where Y ij represents the element in the i-th row and j-th column of the admittance matrix, is the complex value of the voltage at the jth node;

[0043] Injection power measurement of node i It can be expressed as follows:

[0044]

[0045] P i represents the injected active power measurement of node i, Q i represents the injected reactive power measurement of node i, is the complex value of the injected current at node i;

[0046] According to the definition of the admittance matrix and the KCL law, the node injection current It can be expressed as:

[0047]

[0048] Among them, Y im represents the element value of the i-th row and m-th column of the admittance matrix, represents the complex value of the voltage at the mth node;

[0049] at this time, and pass Linear association, and pass Linear association, the relationship between the measurement vector z and the state vector x is in the form of z = Gx, G is the transfer matrix, directly solving this linear equation to obtain the complex value of the voltage, and the solution of this equation is the linear state estimation result xL ;

[0050] Furthermore, according to the above results, the sample data is generated in step 3: the node injection power, branch power, and photovoltaic power are used as inputs, and the difference between the linear estimation result and the nonlinear estimation result, that is, the linearization error, is used as output, and the deep learning model is trained offline to obtain a deep learning model that can predict the real-time linearization error, wherein the training settings of the model are as follows:

[0051] (2.1) Input features

[0052] The input characteristics include the node injection power measurement at time t and branch power measurement Photovoltaic power generation at time t

[0053] (2.2) Expected output

[0054] The nonlinear estimation result x calculated by historical data in step 2 is N With the linear estimation result x L The difference between is taken as the expected output, which represents the error of linearized state estimation.

[0055] (2.3) Deep Neural Network Model

[0056] In the forward propagation algorithm, the output of the previous layer of neurons is used as the input of the next layer of neurons, as shown below:

[0057] z (l) =W (l) a (l-1) +b (l)

[0058] a (l) =f(z (l) )

[0059]

[0060] Among them, a (l-1) is the activation value of the l-1th layer, a (0) Indicates input, including photovoltaic power Node injection power Branch power and node voltage W (l) is the weight matrix of the lth layer, a (l) represents the activation value of the lth layer, z (l) represents the output value of the l-1th layer neuron, b (l) is the bias vector of the lth layer, f(·) is the activation function, and φ represents the set of elements;

[0061] The back propagation algorithm compares the estimated state output by the forward propagation with the actual state, calculates the loss function, minimizes the loss function according to the gradient descent method, and updates the weight matrix W. (l) and the bias vector b (l) , the loss function adopts the mean square error function.

[0062] Furthermore, in step 4, the real-time system characteristics are used to calculate the initial linear estimation result using the complex domain linear state estimation method, and the real-time system characteristics are input into the deep learning model trained in step 3 to predict the linearization error. Finally, the error is superimposed on the initial linear state estimation result to obtain the corrected linear state estimation result, which is as follows:

[0063] (3.1) Initial linear state estimation

[0064] The real-time system characteristics include real-time measurement data such as node injection power, branch power and photovoltaic power, which are expressed as:

[0065]

[0066] in, represents the real-time node injection power of the ith node, represents the real-time branch power from node i to node j, Indicates the real-time photovoltaic power;

[0067] The same method as the complex domain linear estimation method for the test distribution network using historical measurement data in step 2 is used to perform linear state estimation of the test distribution network using the acquired real-time measurement data to solve the real-time linear estimation result x L ′, this result is the initial state quantity;

[0068] (3.2) Deep learning model online prediction linearization error

[0069] The real-time system characteristics real As input, it is input into the offline trained deep learning model to predict the linearization error Δx of the current time section L ′, the deep learning model can be expressed as:

[0070] Δx L ′=K DL (z real ; Θ)

[0071] Among them, K DL (·) represents the deep learning model, which has been obtained through offline training; Θ is the model parameter; Δx L ′ is the linearization error output by the deep learning model, that is, the linearization error value of the real-time voltage estimation value;

[0072] (3.3) Error correction

[0073] The predicted linearization error Δx L ′ and the initial linear state estimation result x L ′ is added to obtain the corrected state estimation result x F ′:

[0074] x F ′=x L ′+Δx L ′.

[0075] Furthermore, after the calculation of the current time section described in step 5 is completed, jump to the next time section and repeat step 4 until all time sections are calculated. Usually, a continuous time section state estimation is performed for one day.

[0076] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0077] The present invention proposes a data-driven linear state estimation method based on deep neural networks to cope with the challenges brought by high-penetration photovoltaic power generation in unbalanced distribution networks. Traditional linear state estimation methods will result in reduced accuracy due to fluctuations in the linearization process and photovoltaic power generation output. To address this problem, the present invention uses a deep neural network model to correct the linearization error, thereby improving the accuracy of state estimation. The deep neural network model is trained using historical measurements and state estimation results to form an error correction model that can adapt to real-time requirements. The present invention provides a new solution for distribution network state estimation under high-penetration photovoltaic power generation conditions. By combining physical modeling with data-driven methods, the accuracy and practicality of state estimation are effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a flow chart of the data-driven linear state estimation method based on deep neural network according to the present invention;

[0079] Figure 2 It is a speed measurement system diagram of a 123-node three-phase unbalanced distribution network;

[0080] Figure 3 It is the comparison of the estimated values ​​before and after adding data drive to each phase of node 40. (a) (b) (c) are the CWLS estimation results, and (d) (e) (f) are the CWLAV estimation results;

[0081] Figure 4 The mean absolute error statistics of the estimation results under three weather conditions (sunny, cloudy, and rainy). (a) is the effect diagram of DCWLS, and (b) is the effect diagram of DCWLAV.

[0082] Figure 5 These are the photovoltaic power curves under three weather conditions. DETAILED DESCRIPTION

[0083] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0084] like Figure 1 As shown, the present invention proposes a data-driven linear state estimation method based on a deep neural network, the method comprising the following steps:

[0085] Step 1: construct a basic information set required for data input according to parameter information of a three-phase unbalanced distribution network;

[0086] Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic distribution network to be tested, including node injection power, branch power, and photovoltaic power. Use the above historical data to perform state estimation on the distribution network to be tested using linear estimation method and nonlinear estimation method, respectively, to obtain linear estimation results and nonlinear estimation results;

[0087] Step 3: Generate sample data based on the above results: take the node injection power, branch power, and photovoltaic power as input, take the difference between the linear estimation result and the nonlinear estimation result, i.e., the linearization error, as output, train the deep learning model offline, and obtain a deep learning model that can predict the real-time linearization error;

[0088] Step 4: Utilize the real-time system characteristics and the complex domain linear state estimation method to calculate the initial linear estimation result, input the real-time system characteristics into the deep learning model trained in step 3, predict the linearization error, and finally superimpose the error onto the initial linear state estimation result to obtain the corrected linear state estimation result;

[0089] Step 5: After the calculation of the current time section is completed, jump to the next time section and repeat step 4 until all time sections are calculated.

[0090] Furthermore, step 1 constructs a basic information set required for data input based on parameter information of the three-phase unbalanced distribution network, and the parameter information includes resistance and reactance of the three-phase branches of the distribution network, equivalent resistance and reactance of the power supply model, and equivalent resistance and reactance of the transformer, wherein the resistance and reactance of the three-phase branches of the distribution network are electrical parameters of each three-phase branch, which are used to describe the loss characteristics of electric energy during transmission; the equivalent resistance and reactance of the power supply model are used to characterize the characteristics of the power supply network; the equivalent resistance and reactance of the transformer are used to describe the performance and influence of the transformer; and the node admittance matrix of the system to be tested is calculated and generated based on the above parameters.

[0091] Furthermore, in step 2, the linear estimation method and the nonlinear estimation method are used to estimate the state of the distribution network to be tested. The specific methods are as follows:

[0092] (1.1) Nonlinear state estimation

[0093] The nonlinear state estimation method is performed in the polar coordinate system, and the state variables are the voltage amplitude and voltage phase angle as shown below:

[0094]

[0095] Where x represents the state vector, Represents the kth node Phase voltage amplitude, Represents the kth node Phase voltage angle (k = 1, 2, ..., n), n is the number of system nodes;

[0096] The expression form of the measurement equation is z=h(x)+e, where z represents the measurement vector, h(·) represents the measurement function, and e represents the measurement residual vector. The specific measurement equation should be as follows:

[0097]

[0098] In the formula, and The i-th node is Phase injected active power measurement and reactive power measurement, and They are the branches from node i to node j. Phase branch active power measurement and reactive power measurement, and They are respectively the admittance matrices The real and imaginary parts of the elements between phase and ψ, Represents the i-th node Phase voltage amplitude, represents the voltage amplitude of the ψ phase at the i-th node, represents the voltage amplitude of the jth node ψ phase, is the i-th node The phase angle difference between the phase and the j-th node ψ;

[0099] The weighted least squares method is used for state estimation. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). By iterative solution, the state quantity that minimizes the objective function is obtained. The vector form of the objective function is as follows:

[0100] minJ=[zh(x)] T R-1 [zh(x)]

[0101] Among them, J is the objective function, R is the standard deviation of the measurement noise, and its reciprocal is taken as the weight value;

[0102] Taking the partial derivative of the above formula with respect to x and setting it to zero, we get:

[0103] H(x)R -1 [zh(x)]=0

[0104] Among them, H(x) is the Jacobian matrix of the measurement function, and the specific expression is:

[0105]

[0106] Using Taylor series, the nonlinear measurement function is converted to (0) Expand at x (0) is the selected system initial value, and the following formula is used for iterative solution:

[0107] x (p+1) =x (p) +[H T (x (p) )R -1 H(x (p) )] -1 H T (x (p) )R -1 [zh(x (p) )]

[0108] where x (p) and x (p+1) are the state quantities obtained by solving the pth and p+1th iterations respectively;

[0109] The iteration stops when convergence occurs, that is, x (p+1) -x (p) The difference between (p+1) That is, the state quantity required to minimize the objective function The final solution obtained by this method is the nonlinear state estimate x N ;

[0110] (1.2) Linear state estimation

[0111] The linear state estimation is performed in the complex domain, and the state variables are complex values ​​of voltage, as follows:

[0112]

[0113] in, is the kth node The complex value of the phase voltage is expressed as Represents complex values The real part of Represents complex values The imaginary part of

[0114] For the linear state estimation in the complex domain, the node injection power measurement and branch power measurement are both in complex form and the calculation is completed in the complex domain;

[0115] Complex power measurement of the branch from node i to node j It is expressed as follows:

[0116]

[0117] Among them, P ij represents the active power measurement of the branch from node i to node j, Q ij represents the reactive power measurement of the branch from node i to node j, represents the complex value of the voltage at the ith node, represents the complex value of the current in the branch from node i to node j, and the superscript * indicates that the conjugate is taken;

[0118] According to the definition of the admittance matrix, the branch current It can be obtained by the following formula:

[0119]

[0120] where Y ij represents the element in the i-th row and j-th column of the admittance matrix, is the complex value of the voltage at the jth node;

[0121] Injection power measurement of node i It can be expressed as follows:

[0122]

[0123] P i represents the injected active power measurement of node i, Q i represents the injected reactive power measurement of node i, is the complex value of the injected current at node i;

[0124] According to the definition of the admittance matrix and the KCL law, the node injection current It can be expressed as:

[0125]

[0126] Among them, Y im represents the element value of the i-th row and m-th column of the admittance matrix, represents the complex value of the voltage at the mth node;

[0127] at this time, and pass Linear association, and pass Linear association, the relationship between the measurement vector z and the state vector x is in the form of z = Gx, G is the transfer matrix, directly solving this linear equation to obtain the complex value of the voltage, and the solution of this equation is the linear state estimation result x L .

[0128] Furthermore, according to the above results, the sample data is generated in step 3: the node injection power, branch power, and photovoltaic power are used as inputs, and the difference between the linear estimation result and the nonlinear estimation result, that is, the linearization error, is used as output, and the deep learning model is trained offline to obtain a deep learning model that can predict the real-time linearization error, wherein the training settings of the model are as follows:

[0129] (2.1) Input features

[0130] The input characteristics include the node injection power measurement at time t and branch power measurement Photovoltaic power generation at time t

[0131] (2.2) Expected output

[0132] The nonlinear estimation result x calculated by historical data in step 2 is N With the linear estimation result x L The difference between is taken as the expected output, which represents the error of linearized state estimation.

[0133] (2.3) Deep Neural Network Model

[0134] In the forward propagation algorithm, the output of the previous layer of neurons is used as the input of the next layer of neurons, as shown below:

[0135] z (l) =W (l) a (l-1) +b (l)

[0136] a (l) =f(z (l) )

[0137]

[0138] Among them, a (l-1) is the activation value of the l-1th layer, a (0)Indicates input, including photovoltaic power Node injection power Branch power and node voltage W (l) is the weight matrix of the lth layer, a (l) represents the activation value of the lth layer, z (l) represents the output value of the l-1 layer neuron, b (l) is the bias vector of the lth layer, f(·) is the activation function, and φ represents the set of elements;

[0139] The back propagation algorithm compares the estimated state output by the forward propagation with the actual state, calculates the loss function, minimizes the loss function according to the gradient descent method, and updates the weight matrix W. (l) and the bias vector b (l) , the loss function adopts the mean square error function.

[0140] Furthermore, in step 4, the real-time system characteristics are used to calculate the initial linear estimation result using the complex domain linear state estimation method, and the real-time system characteristics are input into the deep learning model trained in step 3 to predict the linearization error. Finally, the error is superimposed on the initial linear state estimation result to obtain the corrected linear state estimation result, which is as follows:

[0141] (3.1) Initial linear state estimation

[0142] The real-time system characteristics include real-time measurement data such as node injection power, branch power and photovoltaic power, which are expressed as:

[0143]

[0144] in, represents the real-time node injection power of the ith node, represents the real-time branch power from node i to node j, Indicates the real-time photovoltaic power;

[0145] The same method as the complex domain linear estimation method for the test distribution network using historical measurement data in step 2 is used to perform linear state estimation of the test distribution network using the acquired real-time measurement data to solve the real-time linear estimation result x L ′, this result is the initial state quantity;

[0146] (3.2) Deep learning model online prediction linearization error

[0147] The real-time system characteristics real As input, it is input into the offline trained deep learning model to predict the linearization error Δx of the current time section L′, the deep learning model can be expressed as:

[0148] Δx L ′=K DL (z real ; Θ)

[0149] Among them, K DL (·) represents the deep learning model, which has been obtained through offline training; Θ is the model parameter; Δx L ′ is the linearization error output by the deep learning model, that is, the linearization error value of the real-time voltage estimation value;

[0150] (3.3) Error correction

[0151] The predicted linearization error Δx L ′ and the initial linear state estimation result x L ′ is added to obtain the corrected state estimation result x F ′:

[0152] x F ′=x L ′+Δx L '

[0153] Furthermore, after the calculation of the current time section described in step 5 is completed, jump to the next time section and repeat step 4 until all time sections are calculated. Usually, a continuous time section state estimation is performed for one day.

[0154] Case Analysis

[0155] 1) Example description

[0156] The test system of the present invention is a 123-node three-phase unbalanced distribution network, and the system structure is as follows: Figure 2 As shown. Nodes 2, 16, 29, 57, 88 and 106 in the DC distribution network are connected to distributed photovoltaics, and their power generation capacities are 32MW, 36MW, 30MW, 42MW, 30MW and 48MW respectively. The measurement configuration of the distribution network is as follows: 1) 25% of the branch lines are configured with SCADA measurement; 2) All nodes are configured with AMI measurement. Among them, the uncertainty level of SCADA voltage measurement is 1%, the uncertainty level of SCADA branch power measurement is 0.5%, and the uncertainty level of AMI node injection power measurement is 1%. The load and power generation information is taken from the actual operation data of a local distribution network.

[0157] 2) Comparison of the algorithm of the present invention with other methods

[0158] There are two main groups of comparison algorithms, one is the comparison of traditional WLS, complex-valued WLS (CWLS) and complex-domain data-driven WLS (DCWLS), and the other is the comparison of traditional WLAV, complex-valued WLAV (CWLAV) and complex-domain data-driven WLAV (DCWLAV). Two groups of comparison algorithms and the data-driven linear state estimation method based on deep neural network proposed in this invention are used in each time section. The average absolute error (AverageAbsolute Error, AAE) is used to measure the estimation accuracy:

[0159]

[0160] Where: D is the number of repetitions of the simulation test (all subsequent tests are repeated 50 times, i.e. D = 50), T is the number of sampling points in the test, and N is the number of state variables; is the estimated state value of the i-th node at sampling point t, is the true value of the power flow at the ith node at sampling point t.

[0161] 3) Estimated effect

[0162] There are many nodes in the three-phase distribution network, and the addition of photovoltaics will increase the complexity of state estimation. Therefore, calculation accuracy and efficiency are two important criteria to ensure the actual engineering application of the algorithm. At the same time, the deep neural network model proposed in this invention is suitable for different weather conditions, and the generalization of the model will also be verified.

[0163] The verification method for calculation accuracy is as follows:

[0164] After the experiment was repeated 50 times, the true value, nonlinear estimation value, linear estimation value and data-driven linear estimation value of the three-phase voltage amplitude of the node were analyzed. Figure 3 The comparison of the estimated values ​​before and after adding data driving to CWLS and CWLAV of each phase at node 40 is shown. The average absolute errors of the amplitude and phase angle of the nodes in the entire network are shown in Table 1. Since the complex domain linearization method is used in the calculation process, the linear state estimation results deviate more from the true value than the nonlinear state estimation results. After adding the data driving part, the deviation of the linear state estimation results is significantly reduced.

[0165] Table 1 Average absolute error of the amplitude and phase angle of nodes in the whole network

[0166]

[0167] The verification method for calculation efficiency is as follows:

[0168] Table 2 lists the calculation time of WLS and WLAV under different calculation conditions. The calculation amount of nonlinear state estimation is large and the calculation time is long, so it is difficult to ensure the real-time performance of state estimation calculation. Compared with nonlinear state estimation, the calculation speed of linear state estimation is much faster. Nonlinear WLS involves solving a set of nonlinear equations. The number of iterations and the complexity of each iteration may lead to a significant increase in the amount of calculation, while linear WLS can get the result with just one solution. In addition, the WLAV method requires solving a linear programming problem. Among all the calculation methods, the calculation time of nonlinear WLAV is the longest. Linear WLAV can shorten the calculation time. After adding the data-driven method, the error correction part only increases the amount of calculation by a small amount. The calculation efficiency of the linear method with error correction is still higher than that of the nonlinear method.

[0169] Table 2 Comparison of calculation time of each algorithm under different calculation conditions

[0170]

[0171] The verification method for model generalization is as follows:

[0172] In order to test the performance of the method proposed in the present invention under different weather conditions, the photovoltaic power curves under other typical weather conditions are used for testing. The photovoltaic power curves under three weather conditions (sunny, cloudy, rainy) are shown in FIG. Figure 3 The mean absolute error of the estimated results is Figure 4 and as shown in Table IV.

[0173] Table 3 Average absolute error of estimation results under different weather conditions

[0174]

[0175]

Claims

1. A data-driven linear state estimation method based on deep neural network, characterized in that: The method comprises the following steps: Step 1: construct a basic information set required for data input according to parameter information of a three-phase unbalanced distribution network; Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic distribution network to be tested, including node injection power, branch power, and photovoltaic power. Use the above historical data to perform state estimation on the distribution network to be tested using linear estimation method and nonlinear estimation method, respectively, to obtain linear estimation results and nonlinear estimation results; Step 3: Generate sample data based on the above results: take the node injection power, branch power, and photovoltaic power as input, take the difference between the linear estimation result and the nonlinear estimation result, i.e., the linearization error, as output, train the deep learning model offline, and obtain a deep learning model that predicts the real-time linearization error; Step 4: Utilize the real-time system characteristics and the complex domain linear state estimation method to calculate the initial linear estimation result, input the real-time system characteristics into the deep learning model trained in step 3, predict the linearization error, and superimpose the error on the initial linear state estimation result to obtain the corrected linear state estimation result; Step 5: After the calculation of the current time section is completed, jump to the next time section and repeat step 4 until all time sections are calculated.

2. According to the data-driven linear state estimation method based on deep neural network in claim 1, it is characterized in that: The basic information set required for data input is constructed according to the parameter information of the three-phase unbalanced distribution network as described in step 1, and the parameter information includes the resistance and reactance of the three-phase branches of the distribution network, the equivalent resistance and reactance of the power supply model, and the equivalent resistance and reactance of the transformer, wherein the resistance and reactance of the three-phase branches of the distribution network are electrical parameters of each three-phase branch, which are used to describe the loss characteristics of electric energy during transmission; the equivalent resistance and reactance of the power supply model are used to characterize the characteristics of the power supply network; the equivalent resistance and reactance of the transformer are used to describe the performance and influence of the transformer; and the node admittance matrix of the system to be tested is calculated and generated according to the above parameters.

3. The method of data-driven linear state estimation based on deep neural network according to claim 1, characterized in that: In step 2, the linear estimation method and the nonlinear estimation method are used to estimate the state of the distribution network to be tested. The specific methods are as follows: (1.1) Nonlinear state estimation The nonlinear state estimation method is performed in the polar coordinate system, and the state variables are the voltage amplitude and voltage phase angle as shown below: Where x represents the state vector, Represents the kth node Phase voltage amplitude, Represents the kth node Phase voltage angle, k = 1, 2, ..., n, n is the total number of system nodes; The expression form of the measurement equation is z=h(x)+e, where z represents the measurement vector, h(·) represents the measurement function, and e represents the measurement residual vector. The specific measurement equation should be as follows: In the formula, and The i-th node is Phase injected active power measurement and reactive power measurement, and They are the branches from node i to node j. Phase branch active power measurement and reactive power measurement, and They are respectively the admittance matrices The real and imaginary parts of the elements between phase and ψ, Represents the i-th node Phase voltage amplitude, represents the voltage amplitude of the phase ψ at the i-th node, represents the voltage amplitude of the jth node ψ phase, is the i-th node The phase angle difference between the phase and the j-th node ψ; The weighted least squares method is used for state estimation. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). By iterative solution, the state quantity that minimizes the objective function is obtained. The vector form of the objective function is as follows: minJ=[zh(x)] T R -1 [zh(x)] Among them, J is the objective function, R is the standard deviation of the measurement noise, and its reciprocal is taken as the weight value; Taking the partial derivative of the above formula with respect to x and setting it to zero, we get: H(x)R -1 [z-h(x)]=0 Among them, H(x) is the Jacobian matrix of the measurement function, and the specific expression is: Using Taylor series, the nonlinear measurement function is converted to (0) Expand at x (0) is the selected system initial value, and the following formula is used for iterative solution: x (p+1) =x (p) +[H T (x (p) )R -1 H(x (p) )] -1 H T (x (p) )R -1 [z-h(x (p) )] Among them, x (p) and x (p+1) are the state quantities obtained by solving the pth and p+1th iterations respectively; The iteration stops when convergence occurs, that is, x (p+1) -x (p) The difference of x (p+1) That is, the state quantity required to minimize the objective function The final solution is obtained by this method, which is the nonlinear state estimate x N ; (1.2) Linear state estimation The linear state estimation is performed in the complex domain, and the state variables are complex values ​​of voltage, as follows: in, is the kth node The complex value of the phase voltage is expressed as Represents complex values The real part of Represents complex values The imaginary part of For the linear state estimation in the complex domain, the node injection power measurement and branch power measurement are both in complex form and the calculation is completed in the complex domain; Complex power measurement of the branch from node i to node j It is expressed as follows: Among them, P ij represents the active power measurement of the branch from node i to node j, Q ij represents the reactive power measurement of the branch from node i to node j, represents the complex value of the voltage at the ith node, represents the complex value of the current in the branch from node i to node j, and the superscript * indicates that the conjugate is taken; According to the definition of the admittance matrix, the branch current Calculated by the following formula: Among them, Y ij represents the element in the i-th row and j-th column of the admittance matrix, is the complex value of the voltage at the jth node; Injection power measurement of node i It is expressed as follows: Among them, P i represents the injected active power measurement of node i, Q i represents the injected reactive power measurement of node i, is the complex value of the injected current at node i; According to the definition of the admittance matrix and the KCL law, the node injection current It is expressed as: Among them, Y im represents the element value of the i-th row and m-th column of the admittance matrix, represents the complex value of the voltage at the mth node; at this time, and pass Linear association, and pass Linear association, the relationship between the measurement vector z and the state vector x is in the form of z = Gx, G is the transfer matrix, solving this linear equation to obtain the complex value of the voltage, and the solution of this equation is the linear state estimation result x L .

4. The method of data-driven linear state estimation based on deep neural network according to claim 3, characterized in that: According to the above results, the sample data is generated in step 3: the node injection power, branch power, and photovoltaic power are used as inputs, and the difference between the linear estimation result and the nonlinear estimation result, that is, the linearization error, is used as output. The deep learning model is trained offline to obtain a deep learning model that can predict the real-time linearization error. The training settings of the model are as follows: (2.1) Input features The input characteristics include the node injection power measurement at time t and branch power measurement Photovoltaic power generation at time t (2.2) Expected output The nonlinear estimation result x calculated by historical data in step 2 is N With the linear estimation result x L The difference between is taken as the expected output, which represents the error of linearized state estimation. (2.3) Deep Neural Network Model In the forward propagation algorithm, the output of the previous layer of neurons is used as the input of the next layer of neurons, as shown below: z (l) =W (l) a (l-1) +b (l) a (l) =f(z (l) ) Among them, a (l-1) is the activation value of the l-1th layer, a (0) Indicates input, including photovoltaic power Node injection power Branch power and node voltage W (l) is the weight matrix of the lth layer, a (l) represents the activation value of the lth layer, z (l) represents the output value of the l-1 layer neuron, b (l) is the bias vector of the lth layer, f(·) is the activation function, and φ represents the set of elements; The back propagation algorithm compares the estimated state output by the forward propagation with the actual state, calculates the loss function, minimizes the loss function according to the gradient descent method, and updates the weight matrix W. (l) and the bias vector b (l) , the loss function adopts the mean square error function.

5. The method of data-driven linear state estimation based on deep neural network according to claim 4, characterized in that: In step 4, the real-time system characteristics are used to calculate the initial linear estimation result using the complex domain linear state estimation method, and the real-time system characteristics are input into the deep learning model trained in step 3 to predict the linearization error. Finally, the error is superimposed on the initial linear state estimation result to obtain the corrected linear state estimation result, which is as follows: (3.1) Initial linear state estimation The real-time system characteristics include real-time measurement data such as node injection power, branch power and photovoltaic power, which are expressed as: in, represents the real-time node injection power of the ith node, represents the real-time branch power from node i to node j, Indicates the real-time photovoltaic power; The same method as the complex domain linear estimation method for the test distribution network using historical measurement data in step 2 is used to perform linear state estimation of the test distribution network using the acquired real-time measurement data to solve the real-time linear estimation result x L ′, this result is the initial state quantity; (3.2) Deep learning model online prediction linearization error The real-time system characteristics real As input, it is input into the offline trained deep learning model to predict the linearization error Δx of the current time section L ′, the deep learning model can be expressed as: Δx L ′=K DL (z real ;Θ) Among them, K DL (·) represents the deep learning model, which has been obtained through offline training; Θ is the model parameter; Δx L ′ is the linearization error output by the deep learning model, that is, the linearization error value of the real-time voltage estimation value; (3.3) Error correction The predicted linearization error Δx L ′ and the initial linear state estimation result x L ′ is added to obtain the corrected state estimation result x F ′: x F ′=x L ′+Δx L ′。 6. The method of data-driven linear state estimation based on deep neural network according to claim 1, characterized in that: Step 5 is the continuous time section state estimation for one day.

Images