A data-driven linear state estimation method based on deep neural networks

Abstract

The application discloses a data-driven linear state estimation method based on a deep neural network. The method firstly performs linear state estimation on a distribution network in a complex domain, and generates an error correction model based on historical measurement data and state estimation results; then, the linear state estimation part and the error correction model are connected in series, and a data-driven method is used to correct the error of the linear state estimation result. The algorithm provided by the application can accurately and efficiently solve the state quantity of the distribution network in a three-phase unbalanced distribution network with a high proportion of new energy penetration, thereby providing technical support for real-time acquisition of distribution network information.

Description

Technical Field

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

[0002] With the global energy transition, the penetration rate of distributed photovoltaic (PV) power generation in distribution networks has increased significantly. The high proportion of renewable energy integration has altered the operational characteristics of distribution networks, posing challenges to power balance, voltage stability, and power quality. PV power generation is characterized by volatility and randomness, significantly influenced by weather, seasons, and other factors, greatly increasing the complexity of distribution network state estimation. In real-time monitoring of distribution networks, state estimation is a key technology for providing reliable state information, which can be used for system optimization and fault diagnosis. However, traditional state estimation methods have limitations in addressing the volatility of distributed PV power generation, especially over continuous time sections, where rapid changes in PV power can lead to large estimation errors, affecting system efficiency and security.

[0003] Existing research on state estimation in high-penetration photovoltaic (PV) distribution networks mainly focuses on PV node modeling and robust algorithm exploration, which can be broadly categorized into physical model-based methods and data-driven methods. Physical model-based state estimation typically involves writing out the measurement equations described by the physical model and then calculating state variables from known measurements (such as power and current) using existing methods. Similarly, existing power system state estimation methods based on deep neural network (DNN) models select known measurements as input features for training data, with state variables as the desired output, and solve for the state variables through data-driven fitting. Physical model-based methods model the physical characteristics of the distribution network, offering good interpretability, but struggle to balance computational accuracy and efficiency. Data-driven methods can address these issues, but in most cases lack interpretability. Summary of the Invention

[0004] The purpose of this invention is to address the above-mentioned problems by providing a data-driven linear state estimation method based on deep neural networks, which can accurately acquire real-time state information in distribution networks with a high proportion of photovoltaic power. Furthermore, this invention proposes a data-driven error correction model based on deep neural networks, combining the data-driven model with real-time physical model state estimation. This allows for both rapid linear state estimation of the distribution network and the correction of linearization errors using a data-driven approach, ensuring estimation accuracy.

[0005] Technical Solution: To achieve the aforementioned objectives, this invention proposes a data-driven linear state estimation method based on deep neural networks, which includes the following steps:

[0006] Step 1: Construct the basic information set required for data input based on the parameter information of the three-phase unbalanced distribution network;

[0007] Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic power distribution network to be tested, including node injected power, branch power, and photovoltaic power. Using the above historical data, perform state estimation of the power distribution network to be tested using linear estimation method and nonlinear estimation method respectively, and 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 inputs, and take the difference between the linear estimation result and the nonlinear estimation result, i.e. the linearization error, as the output. Train the deep learning model offline to obtain a deep learning model that can predict the real-time linearization error.

[0009] Step 4: Using the real-time system features, calculate the initial linear estimation result using the complex domain linear state estimation method. Input the real-time system features into the deep learning model trained in Step 3 to predict the linearization error. Finally, add the error to the initial linear state estimation result to obtain the corrected linear state estimation result.

[0010] Step 5: After the current time segment is calculated, jump to the next time segment and repeat Step 4 until all time segments are calculated.

[0011] Furthermore, in step 1, the basic information set required for data input is constructed based on the parameter information of the three-phase unbalanced distribution network. This 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. Specifically, the resistance and reactance of the three-phase branches are electrical parameters of each branch, used to describe the loss characteristics of electrical energy during transmission; the equivalent resistance and reactance of the power supply model characterize the characteristics of the power supply network; and the equivalent resistance and reactance of the transformer describe the performance and impact of the transformer. Based on these parameters, the node admittance matrix of the system under test is calculated and generated.

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

[0013] (1.1) Nonlinear state estimation

[0014] The nonlinear state estimation method is performed in polar coordinates, with the state variables being voltage magnitude and voltage phase angle, as shown below:

[0015]

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

[0017] The measurement equation is expressed as 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 These are the i-th nodes. Phase injection active power measurement and reactive power measurement, and These are the branches from node i to node j. Active power measurement and reactive power measurement of the phase branch. and These are the admittance matrices. The real and imaginary parts of the elements alternating with ψ. Represents the i-th node Phase voltage amplitude, Represents the amplitude of the ψ-phase voltage at the i-th node, and represents This represents the amplitude of phase ψ at the j-th node. It is the i-th node The phase angle difference between phase j and phase ψ at node j;

[0021] State estimation is performed using the weighted least squares (WLS) method. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). Through iterative solution, the state variables that minimize the objective function are obtained. The objective function in vector form is as follows:

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

[0023] Where 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 equation with respect to x and setting it to zero, we get:

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

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

[0027]

[0028] Using Taylor series to transform nonlinear measurement functions at x = x (0) Expand at x (0) Given the selected initial system values, 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) These are the state variables obtained from the p-th and p+1-th iterations, respectively;

[0031] Iteration stops when convergence occurs, i.e., x (p+1) -x (p) The difference reaches the accuracy requirement, at which point x (p+1) That is, the state variable that minimizes the objective function. The final solution obtained using this method is the nonlinear state estimate x. N ;

[0032] (1.2) Linear State Estimation

[0033] Linear state estimation is performed in the complex domain, with the state variables being complex values ​​of voltage, as shown below:

[0034]

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

[0036] For linear state estimation in the complex domain, both node injected power measurement and branch power measurement are in complex form and are calculated in the complex domain.

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

[0038]

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

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

[0041]

[0042] Where Y ij This represents the element in the i-th row and j-th column of the admittance matrix. It is the complex value of the voltage at the j-th node;

[0043] Injection power measurement at node i It can be expressed by the following formula:

[0044]

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

[0046] According to the definition of admittance matrix and Kirchhoff's law, the node injection current... It can be represented as:

[0047]

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

[0049] at this time, and pass Linear correlation, and pass In a linear relationship, the relationship between the measurement vector z and the state vector x is in the form z = Gx, where G is the transition matrix. Solving this linear equation directly yields the complex value of the voltage; the solution to this equation is the linear state estimation result x.L ;

[0050] Furthermore, in step 3, based on the above results, sample data is generated: 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, i.e., the linearization error, is used as the output. A deep learning model is trained offline to obtain a deep learning model capable of predicting real-time linearization error. The training settings for the model are as follows:

[0051] (2.1) Input Features

[0052] Input features include the nodal injection power measurement at time t. Branch power measurement Photovoltaic power generation at time t

[0053] (2.2) Expected Output

[0054] The nonlinear estimation result x obtained from historical data in step 2 is used as the basis for the calculation. N Compared with the linear estimation result x L The difference is taken as the expected output, and this difference represents the error of the linearized state estimate;

[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) a is the activation value of the (l-1)th layer. (0) Indicates input, including photovoltaic power. Node Injection Power Branch power and node voltage W (l) Let a be the weight matrix of the l-th layer. (l) z represents the activation value of the l-th layer. (l) b represents the output value of the neuron in layer (l-1). (l) Let f(·) be the bias vector of the l-th layer, f(·) be the activation function, and φ be the set of elements.

[0061] The backpropagation algorithm compares the estimated state output from the forward propagation with the actual state values, calculates the loss function, minimizes the loss function using gradient descent, and updates the weight matrix W. (l) and bias vector b (l) The loss function is the mean squared error function.

[0062] Furthermore, in step 4, the initial linear estimation result is calculated using the complex domain linear state estimation method based on the real-time system characteristics. The real-time system characteristics are then 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, as detailed below:

[0063] (3.1) Initial linear state estimation

[0064] Real-time system characteristics include real-time measurement data such as node injected power, branch power, and photovoltaic power, expressed as:

[0065]

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

[0067] Similar to the complex domain linear estimation method using historical measurement data in step 2, the linear state estimation of the distribution network under test is performed using the acquired real-time measurement data, and the real-time linear estimation result x is solved. L This result is the initial state variable;

[0068] (3.2) Online prediction of linearization error by deep learning model

[0069] Real-time system characteristics z real As input, it is fed into an offline-trained deep learning model to predict the linearization error Δx at the current time segment. L A deep learning model can be represented as:

[0070] Δx L ′=K DL (z real ;Θ)

[0071] Among them, K DL (·) represents a deep learning model that has been trained offline; Θ represents the model parameters; Δx L ′ is the linearization error output by the deep learning model, i.e., the linearization error value of the real-time voltage estimate;

[0072] (3.3) Error Correction

[0073] The predicted linearization error Δx L ′ and the initial linear state estimation result x L The summation yields the corrected state estimation result x. F ′:

[0074] x F ′=x L +Δx L ′.

[0075] Furthermore, after the current time segment calculation is completed in step 5, the process jumps to the next time segment and repeats step 4 until all time segments are calculated. Typically, a continuous time segment state estimation for one day is performed.

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

[0077] This invention proposes a data-driven linear state estimation method based on deep neural networks to address the challenges posed by high-penetration photovoltaic (PV) power generation in unbalanced distribution networks. Traditional linear state estimation methods suffer from decreased accuracy due to the linearization process and fluctuations in PV output. To address this issue, this invention utilizes a deep neural network model to correct linearization errors, thereby improving state estimation accuracy. The deep neural network model is trained using historical measurements and state estimation results to form an error correction model that adapts to real-time requirements. This invention provides a novel solution for distribution network state estimation under high-penetration PV power generation conditions, effectively improving the accuracy and practicality of state estimation by combining physical modeling with a data-driven approach. Attached Figure Description

[0078] Figure 1 This is a flowchart of the data-driven linear state estimation method based on deep neural networks described in this invention;

[0079] Figure 2 This is a diagram of a three-phase unbalanced distribution network speed measurement system with nodes 1, 2, and 3.

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

[0081] Figure 4 These are statistical graphs of the mean absolute error of the estimation results under three weather conditions (sunny, cloudy, and rainy). (a) is the effect graph of DCWLS, and (b) is the effect graph of DCWLAV.

[0082] Figure 5 These are photovoltaic power curves under three weather conditions. Detailed Implementation

[0083] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0084] like Figure 1 As shown, this invention proposes a data-driven linear state estimation method based on deep neural networks, which includes the following steps:

[0085] Step 1: Construct the basic information set required for data input based on the parameter information of the three-phase unbalanced distribution network;

[0086] Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic power distribution network to be tested, including node injected power, branch power, and photovoltaic power. Using the above historical data, perform state estimation of the power distribution network to be tested using linear estimation method and nonlinear estimation method respectively, and 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 inputs, and take the difference between the linear estimation result and the nonlinear estimation result, i.e. the linearization error, as the output. Train the deep learning model offline to obtain a deep learning model that can predict the real-time linearization error.

[0088] Step 4: Using the real-time system features, calculate the initial linear estimation result using the complex domain linear state estimation method. Input the real-time system features into the deep learning model trained in Step 3 to predict the linearization error. Finally, add the error to the initial linear state estimation result to obtain the corrected linear state estimation result.

[0089] Step 5: After the current time segment is calculated, jump to the next time segment and repeat Step 4 until all time segments are calculated.

[0090] Furthermore, in step 1, the basic information set required for data input is constructed based on the parameter information of the three-phase unbalanced distribution network. 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. Among them, the resistance and reactance of the three-phase branches of the distribution network are the electrical parameters of each three-phase branch, used to describe the loss characteristics of electrical 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 impact of the transformer; and the node admittance matrix of the system under test is calculated based on the above parameters.

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

[0092] (1.1) Nonlinear state estimation

[0093] The nonlinear state estimation method is performed in polar coordinates, with the state variables being voltage magnitude and voltage phase angle, as shown below:

[0094]

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

[0096] The measurement equation is expressed as 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 These are the i-th nodes. Phase injection active power measurement and reactive power measurement, and These are the branches from node i to node j. Active power measurement and reactive power measurement of the phase branch. and These are the admittance matrices. The real and imaginary parts of the elements alternating with ψ. Represents the i-th node Phase voltage amplitude, Represents the amplitude of the ψ-phase voltage at the i-th node, and represents This represents the amplitude of phase ψ at the j-th node. It is the i-th node The phase angle difference between phase j and phase ψ at node j;

[0099] State estimation is performed using the weighted least squares (WLS) method. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). Through iterative solution, the state variables that minimize the objective function are obtained. The objective function in vector form is as follows:

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

[0101] Where 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 equation with respect to x and setting it to zero, we get:

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

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

[0105]

[0106] Using Taylor series to transform nonlinear measurement functions at x = x (0) Expand at x (0) Given the selected initial system values, 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) These are the state variables obtained from the p-th and p+1-th iterations, respectively;

[0109] Iteration stops when convergence occurs, i.e., x (p+1) -x (p) The difference reaches the accuracy requirement, at which point x (p+1) That is, the state variable that minimizes the objective function. The final solution obtained using this method is the nonlinear state estimate x. N ;

[0110] (1.2) Linear State Estimation

[0111] Linear state estimation is performed in the complex domain, with the state variables being complex values ​​of voltage, as shown below:

[0112]

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

[0114] For linear state estimation in the complex domain, both node injected power measurement and branch power measurement are in complex form and are calculated in the complex domain.

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

[0116]

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

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

[0119]

[0120] Where Y ij This represents the element in the i-th row and j-th column of the admittance matrix. It is the complex value of the voltage at the j-th node;

[0121] Injection power measurement at node i It can be expressed by the following formula:

[0122]

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

[0124] According to the definition of admittance matrix and Kirchhoff's law, the node injection current... It can be represented as:

[0125]

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

[0127] at this time, and pass Linear correlation, and pass In a linear relationship, the relationship between the measurement vector z and the state vector x is in the form z = Gx, where G is the transition matrix. Solving this linear equation directly yields the complex value of the voltage; the solution to this equation is the linear state estimation result x. L .

[0128] Furthermore, in step 3, based on the above results, sample data is generated: 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, i.e., the linearization error, is used as the output. A deep learning model is trained offline to obtain a deep learning model capable of predicting real-time linearization error. The training settings for the model are as follows:

[0129] (2.1) Input Features

[0130] Input features include the nodal injection power measurement at time t. Branch power measurement Photovoltaic power generation at time t

[0131] (2.2) Expected Output

[0132] The nonlinear estimation result x obtained from historical data in step 2 is used as the basis for the calculation. N Compared with the linear estimation result x L The difference is taken as the expected output, and this difference represents the error of the linearized state estimate;

[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) a is the activation value of the (l-1)th layer. (0)Indicates input, including photovoltaic power. Node Injection Power Branch power and node voltage W (l) Let a be the weight matrix of the l-th layer. (l) z represents the activation value of the l-th layer. (l) b represents the output value of the neuron in layer (l-1). (l) Let f(·) be the bias vector of the l-th layer, f(·) be the activation function, and φ be the set of elements.

[0139] The backpropagation algorithm compares the estimated state output from the forward propagation with the actual state values, calculates the loss function, minimizes the loss function using gradient descent, and updates the weight matrix W. (l) and bias vector b (l) The loss function is the mean squared error function.

[0140] Furthermore, in step 4, the initial linear estimation result is calculated using the complex domain linear state estimation method based on the real-time system characteristics. The real-time system characteristics are then 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, as detailed below:

[0141] (3.1) Initial linear state estimation

[0142] Real-time system characteristics include real-time measurement data such as node injected power, branch power, and photovoltaic power, expressed as:

[0143]

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

[0145] Similar to the complex domain linear estimation method using historical measurement data in step 2, the linear state estimation of the distribution network under test is performed using the acquired real-time measurement data, and the real-time linear estimation result x is solved. L This result is the initial state variable;

[0146] (3.2) Online prediction of linearization error by deep learning model

[0147] Real-time system characteristics z real As input, it is fed into an offline-trained deep learning model to predict the linearization error Δx at the current time segment. LA deep learning model can be represented as:

[0148] Δx L ′=K DL (z real ;Θ)

[0149] Among them, K DL (·) represents a deep learning model that has been trained offline; Θ represents the model parameters; Δx L ′ is the linearization error output by the deep learning model, i.e., the linearization error value of the real-time voltage estimate;

[0150] (3.3) Error Correction

[0151] The predicted linearization error Δx L ′ and the initial linear state estimation result x L The summation yields the corrected state estimation result x. F ′:

[0152] x F ′=x L +Δx L ′

[0153] Furthermore, after the current time segment calculation is completed in step 5, the process jumps to the next time segment and repeats step 4 until all time segments are calculated. Typically, a continuous time segment state estimation for one day is performed.

[0154] Case Analysis

[0155] 1) Example Explanation

[0156] The test system of this 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 photovoltaic (PV) systems, with generating capacities of 32MW, 36MW, 30MW, 42MW, 30MW, and 48MW, respectively. The measurement configuration for this distribution network is as follows: 1) 25% of the branch lines are equipped with SCADA measurements; 2) all nodes are equipped with AMI measurements. The uncertainty level for SCADA voltage measurements is 1%, the uncertainty level for SCADA branch power measurements is 0.5%, and the uncertainty level for AMI node injected power measurements is 1%. Load and generation power information are obtained from actual operating data of a local distribution network.

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

[0158] The comparison algorithms are mainly divided into two groups: one group compares traditional WLS, complex-valued WLS (CWLS), and data-driven complex-valued WLS (DCWLS); the other group compares traditional WLAV, complex-valued WLAV (CWLAV), and data-driven complex-valued WLAV (DCWLAV). At each time segment, both comparison algorithms and the data-driven linear state estimation method based on deep neural networks proposed in this invention are used. The estimation accuracy is measured using the mean absolute error (AAE).

[0159]

[0160] In the formula: 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; It is the state estimate of the i-th node at sampling point t. It is the true power flow value of the i-th node at sampling point t.

[0161] 3) Estimating the effect

[0162] Three-phase distribution networks have numerous nodes, and the addition of photovoltaics increases the complexity of state estimation. Therefore, computational accuracy and efficiency are two important metrics for ensuring the algorithm's practical engineering applications. Furthermore, the deep neural network model proposed in this invention is applicable to various weather conditions, and its generalization ability will be verified.

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

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

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

[0166]

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

[0168] Table 2 lists the computation time of WLS and WLAV under different computational conditions. Nonlinear state estimation is computationally intensive and time-consuming, making it difficult to guarantee real-time performance. Compared to nonlinear state estimation, linear state estimation is much faster. Nonlinear WLS involves solving a system of nonlinear equations; the number of iterations and the complexity of each iteration can significantly increase the computational load, while linear WLS only requires a single solution. Furthermore, the WLAV method requires solving a linear programming problem, and among all computational methods, nonlinear WLAV has the longest computation time. Linear WLAV can shorten the computation time. After adding a data-driven approach, the error correction part only adds a small amount of computation; the computational efficiency of the linear method with error correction is still higher than that of the nonlinear method.

[0169] Table 2 Comparison of computation time for each algorithm under different computational conditions

[0170]

[0171] The following methods are used to verify the generalization ability of the model:

[0172] To test the performance of the method proposed in this invention under different weather conditions, photovoltaic power curves under other typical weather conditions were used for testing. The photovoltaic power curves under three weather conditions (sunny, cloudy, and rainy) are shown below. Figure 3 The mean absolute error of the estimation results is as follows: Figure 4 As shown in Table IV.

[0173] Table 3. Mean Absolute Error of Estimation Results under Different Weather Conditions

[0174]

[0175]

Claims

1. A data-driven linear state estimation method based on deep neural networks, characterized in that, The method includes the following steps: Step 1: Construct the basic information set required for data input based on the parameter information of the three-phase unbalanced distribution network; Step 2: Extract the measured values ​​of each time section from the historical data of the distributed photovoltaic power distribution network to be tested, including node injected power, branch power, and photovoltaic power. Using the above historical data, perform state estimation of the power distribution network to be tested using linear estimation method and nonlinear estimation method respectively, and 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 inputs, and take the difference between the linear estimation result and the nonlinear estimation result, i.e. the linearization error, as the output. Train the deep learning model offline to obtain a deep learning model that predicts the real-time linearization error. Step 4: Utilize the real-time system features and use the complex domain linear state estimation method to calculate the initial linear estimation result. Input the real-time system features into the deep learning model trained in Step 3 to predict the linearization error. Add the error to the initial linear state estimation result to obtain the corrected linear state estimation result. Step 5: After the current time segment is calculated, jump to the next time segment and repeat Step 4 until all time segments are calculated.

2. The data-driven linear state estimation method based on deep neural networks according to claim 1, characterized in that, Step 1 involves constructing the basic information set required for data input based on the parameter information of the three-phase unbalanced distribution network. This 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. Specifically, the resistance and reactance of the three-phase branches are electrical parameters of each branch, used to describe the loss characteristics of electrical energy during transmission; the equivalent resistance and reactance of the power supply model characterize the characteristics of the power supply network; and the equivalent resistance and reactance of the transformer describe the performance and impact of the transformer. Based on these parameters, the node admittance matrix of the system under test is calculated.

3. The data-driven linear state estimation method based on deep neural networks according to claim 1, characterized in that, In step 2, the state estimation of the distribution network under test is performed using both linear and nonlinear estimation methods, as detailed below: (1.1) Nonlinear state estimation The nonlinear state estimation method is performed in polar coordinates, with the state variables being voltage magnitude and voltage phase angle, as shown below: Where x represents the state vector. Represents the k-th node Phase voltage amplitude, Represents the k-th node Phase voltage phase angle, k = 1, 2, ..., n, where n is the total number of system nodes; The measurement equation is expressed as 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 These are the i-th nodes. Phase injection active power measurement and reactive power measurement, and These are the branches from node i to node j. Active power measurement and reactive power measurement of the phase branch. and These are the admittance matrices. The real and imaginary parts of the elements alternating with ψ. Represents the i-th node Phase voltage amplitude, This represents the amplitude of phase ψ at the i-th node. This represents the amplitude of the ψ-phase voltage at the j-th node. It is the i-th node The phase angle difference between phase j and phase ψ at node j; State estimation is performed using the weighted least squares (WLS) method. The objective function of WLS is to minimize the weighted sum of squares of the residual vector e = zh(x). Through iterative solution, the state variables that minimize the objective function are obtained. The objective function in vector form is as follows: minJ=[zh(x)] T R -1 [zh(x)] Where 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 equation with respect to x and setting it to zero, we get: H(x)R -1 [z-h(x)]=0 Where H(x) is the Jacobian matrix of the measurement function, and its specific expression is: Using Taylor series to transform nonlinear measurement functions at x = x (0) Expand at x (0) Given the selected initial system values, 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) )] Where, x (p) and x (p+1) These are the state variables obtained from the p-th and p+1-th iterations, respectively; Iteration stops when convergence occurs, i.e., x (p+1) -x (p) The difference reaches the accuracy requirement, at which point x (p+1) That is, the state variable that minimizes the objective function. The final solution obtained using this method is the nonlinear state estimate x. N ; (1.2) Linear State Estimation Linear state estimation is performed in the complex domain, with the state variables being complex values ​​of voltage, as shown below: in, It is the kth node The complex value of the phase voltage is expressed as: Represents complex values The real part, Represents complex values The imaginary part; For linear state estimation in the complex domain, both node injected power measurement and branch power measurement are in complex form and are calculated in the complex domain. Complex power measurement of the branch from node i to node j Expressed as follows: Among them, P ij Q represents the active power measurement of the branch from node i to node j. ij This represents the reactive power measurement of the branch from node i to node j. Let represent the complex value of the voltage at the i-th node. This represents the complex value of the current in the branch from node i to node j, and the superscript * indicates that its conjugate is taken. According to the definition of admittance matrix, branch current It can be obtained using the following formula: Among them, Y ij This represents the element in the i-th row and j-th column of the admittance matrix. It is the complex value of the voltage at the j-th node; Injection power measurement at node i Expressed as follows: Among them, P i Q represents the injected active power measurement at node i. i This indicates the measurement of injected reactive power at node i. It is the complex value of the injected current at node i; According to the definition of admittance matrix and Kirchhoff's law, the node injection current... Represented as: Among them, Y im Let represent the value of the element in the i-th row and m-th column of the admittance matrix. This represents the complex value of the voltage at the m-th node; at this time, and pass Linear correlation, and pass In a linear relationship, the relationship between the measurement vector z and the state vector x is of the form z = Gx, where G is the transition matrix. Solving this linear equation yields the complex value of the voltage. The solution to this equation is the linear state estimation result x. L .

4. The data-driven linear state estimation method based on deep neural networks according to claim 3, characterized in that, Step 3 involves generating sample data based on the above results: Node injection power, branch power, and photovoltaic power are used as inputs; the difference between the linear estimation result and the nonlinear estimation result, i.e., the linearization error, is used as the output. A deep learning model is trained offline to obtain a deep learning model capable of predicting real-time linearization errors. The model training settings are as follows: (2.1) Input Features Input features include the nodal injection power measurement at time t. Branch power measurement Photovoltaic power generation at time t (2.2) Expected Output The nonlinear estimation result x obtained from historical data in step 2 is used as the basis for the calculation. N Compared with the linear estimation result x L The difference is taken as the expected output, and this difference represents the error of the linearized state estimate; (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) a is the activation value of the (l-1)th layer. (0) Indicates input, including photovoltaic power. Node Injection Power Branch power and node voltage W (l) Let a be the weight matrix of the l-th layer. (l) z represents the activation value of the l-th layer. (l) b represents the output value of the neuron in layer (l-1). (l) Let f(·) be the bias vector of the l-th layer, f(·) be the activation function, and φ be the set of elements. The backpropagation algorithm compares the estimated state output from the forward propagation with the actual state values, calculates the loss function, minimizes the loss function using gradient descent, and updates the weight matrix W. (l) and bias vector b (l) The loss function is the mean squared error function.

5. The data-driven linear state estimation method based on deep neural networks according to claim 4, characterized in that, Step 4 involves using real-time system features and employing a complex-domain linear state estimation method to calculate the initial linear estimation result. The real-time system features are then input into the deep learning model trained in Step 3 to predict the linearization error. Finally, the error is superimposed onto the initial linear state estimation result to obtain the corrected linear state estimation result, as detailed below: (3.1) Initial linear state estimation Real-time system characteristics include real-time measurement data such as node injected power, branch power, and photovoltaic power, expressed as: in, This represents the real-time node injection power of the i-th node. This represents the real-time branch power from node i to node j. Indicates real-time photovoltaic power; Similar to the complex domain linear estimation method using historical measurement data in step 2, linear state estimation of the distribution network under test is performed using the acquired real-time measurement data, and the real-time linear estimation result x is solved. L This result is the initial state variable; (3.2) Online prediction of linearization error by deep learning model Real-time system characteristics z real As input, it is fed into an offline-trained deep learning model to predict the linearization error Δx at the current time segment. L A deep learning model can be represented as: Δx L ′=K DL (z real ;Θ) Among them, K DL (·) represents a deep learning model that has been trained offline; Θ represents the model parameters; Δx L ′ is the linearization error output by the deep learning model, i.e., the linearization error value of the real-time voltage estimate; (3.3) Error Correction The predicted linearization error Δx L ′ and the initial linear state estimation result x L The summation yields the corrected state estimate x. F ′: x F ′=x L ′+Δx L ′。 6. The data-driven linear state estimation method based on deep neural networks according to claim 1, characterized in that, Step 5 involves estimating the state of a continuous time section over a day.

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