Initial value calculation method for distribution network state estimation based on simplified power flow neural network

Abstract

The present invention discloses a method for calculating the initial value of distribution network state estimation based on a simplified power flow neural network. This method uses historical data and a neural network embedded with physical knowledge to learn the initial value of the distribution network state variables for the calculation of distribution network state estimation. Since the power flow equation is a non-linear function, it can be described by a fully-connected neural network with measurements as inputs and state variables as outputs. This method proposes a physics-aware neural network based on a simplified power flow equation, that is, using the knowledge related to the distribution network topology structure to prune the fully-connected neural network and remove its unnecessary parameters; then using historical data to offline train the pruned network; after that, inputting real-time measurement data into the network to obtain a more accurate initial value for use in the initial value of the Gauss-Newton method; finally, the distribution network state estimation can be iteratively solved according to the Gauss-Newton method.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution network state estimation, and relates to a method for calculating the state of a distribution network based on historical measurement data. Specifically, it relates to a method for calculating the initial value of distribution network state estimation based on a simplified power flow neural network. Background Art

[0002] The actual measurement information of primary equipment in the distribution network needs to be transmitted to the dispatching control center through a telecontrol device. There are certain errors in the measurement itself, and inevitable delays, packet losses and other abnormalities will also occur in each link during the data transmission process. There are a large number of primary equipment in the distribution network, and from the perspective of cost control, the configuration of measurement points, measurement accuracy, acquisition frequency, communication transmission channels and data transmission frequency are all restricted. Therefore, the control dispatching center often cannot obtain complete and sufficient data required for power system calculation and analysis.

[0003] To solve the above problems, in addition to continuously improving the measurement device and transmission system, mathematical processing methods can also be used to improve the integrity and reliability of measurement data. Distribution System State Estimation (DSSE) is a method for restoring the state variables of a distribution network system through limited measurement data, and is the basis for the online application of the Supervisory Control and Data Acquisition (SCADA) system and the Energy Management System (EMS). The general steps of DSSE are as follows: First, determine the dynamic topology of the distribution network according to the telecommunication information, and then estimate the system state variables that conform to circuit theory based on the telemetry information, including node voltage phasors, branch powers, etc.

[0004] Existing methods for distribution network state estimation are mainly divided into the least squares method, the least mean square algorithm, the least trimmed squares method, and the least absolute value method. The least mean square algorithm and the least trimmed squares method require a large amount of computational cost during the calculation process. Among them, the least mean square algorithm requires a high redundancy of distribution network measurements, and the least trimmed squares algorithm has a very large memory requirement. Although the least absolute value can automatically reject bad data and has robustness, it also requires a large amount of computational resources when performing estimation calculations. Therefore, the least squares method has become the most traditional state estimation modeling method in the power system. Because of its fast and simple advantages, it is widely used in the state estimation of the power system; and the Gauss-Newton method is the most common algorithm used to solve the least squares method, but this algorithm is sensitive to the initial value and may lead to non-convergence. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technologies, the present invention proposes a method for calculating the initial value of the distribution network state estimation based on a simplified power flow neural network. According to the numerical relationship between the distribution network structure and variables, a neural network is pruned based on the simplified power flow equation to reduce the computational amount. Subsequently, the initial value of the distribution network state estimation output by the neural network can be applied to the Gauss-Newton method to solve the non-convergence problem caused by unreasonable initial value setting.

[0006] The method for calculating the initial value of the distribution network state estimation based on a simplified power flow neural network specifically includes the following steps:

[0007] Step 1: Establish a BP neural network, including an input layer, a hidden layer, and an output layer. Among them, the number of neurons in the input layer is equal to the number of measurements in the distribution network, and the number of neurons in the output layer is equal to the number of state variables in the distribution network.

[0008] Step 2: For a power system with n nodes, its AC power flow in polar coordinates is expressed as:

[0009]

[0010] where P i , Q i are the active power and reactive power of node i respectively; V i , V j represent the voltage amplitudes of nodes i and j respectively, θ ij is the phase angle difference between node i and node j, and i, j = 1, 2,..., n; G ij +jB ij =Y ij , Y ij represents the element in the node admittance matrix Y, and G ij , B ij represent the real part and imaginary part of the element in the i-th row and j-th column of the node admittance matrix Y respectively.

[0011] In the power system, the voltage amplitudes of nodes are approximately 1 p.u. At the same time, the phase angles of the voltages at both ends of the line rarely exceed 30°, and most of them are within 10°, that is, there is:

[0012] g ij (V i -V j cosθ ij )≈g ij (V i -V j )

[0013] b ij V j sinθ ij ≈b ij (θ i -θj ) (2)

[0014] where b ij and g ij are the conductance and susceptance between nodes i and j respectively; Substitute Equation (2) into Equation (1), and decouple the voltage magnitude and voltage phase angle according to the active power and reactive power:

[0015]

[0016]

[0017] Converted to matrix representation as:

[0018]

[0019] Step 3: The form of Equation (5) is similar to the decoupled linear power flow, which gives the relationship between the active power P, reactive power Q, voltage magnitude V, and voltage phase angle θ. When Equation (5) has a solution, that is is invertible, then there is:

[0020]

[0021] Since the voltage magnitudes of the nodes in the power system are approximately 1 p.u., so in Equation (6) can be changed to:

[0022]

[0023] Substitute Equation (7) into Equation (6) to get:

[0024]

[0025] Let Decompose the voltage magnitude V and voltage phase angle θ into:

[0026]

[0027] According to formula (9), the voltage phase angle θ and voltage amplitude V can be decomposed into two parts, each of which can be obtained through the voltage amplitude and power injection of the nodes, and there is a certain redundancy in the input. Obviously, the measurement vector can fully represent the voltage amplitude and power injection of the nodes. Since the neurons of the output voltage amplitude are related to the node voltage, the injected active power, and the reactive power, therefore, half of the neurons in the hidden layer are fully connected to the neurons of the node voltage amplitude in the output layer; the node voltage phase angle is the same as the node voltage amplitude, and the other half of the neurons in the hidden layer are fully connected to the neurons of the node voltage phase angle in the output layer. In this way, the non-linear functions of the node voltage amplitude, injected active power, and reactive power with respect to the node voltage phase angle and node voltage amplitude can be obtained. A simplified BP neural network can be obtained.

[0028] Step 4: Since the measurements of the PMU are very accurate, the nodes installed with PMUs can be used as the "dividing lines" for dividing the distribution network topology network, and the distribution network can be divided into several parts. For a distribution network installed with L - 1 PMUs, it can be divided into L parts:

[0029]

[0030] Among them, Y' 11 , Y' 22 ,..., Y' LL are the coefficient admittance matrices of the parts divided by the PMU respectively, and Y' 12 , Y' 21 , Y' 1L , Y' L1 , Y' 2L , Y' L2 are the coefficient admittance matrices of different parts of the PMU respectively. Since there are only very few connection relationships in the radial distribution network at the PMU connection nodes, the coefficient matrix can be considered as a zero matrix.

[0031] According to the divided distribution network topology structure, the simplified BP neural network in Step 3 is divided into multiple groups of neural networks, which not only reduces the parameters of the input layer but also reduces the parameters of the hidden layer, and a BP neural network based on the simplified power flow equation is obtained.

[0032] Step 5: There is a large amount of historical measurement data in the distribution network. Input the historical measurement data of the distribution network into the BP neural network based on the simplified power flow equation. Since the true values of the state variables of the distribution network already exist in the above dataset, set the loss function of the neural network as the MSE loss. The MSE loss is the mean of the sum of the squares of the errors between the predicted data and the corresponding points of the original data, that is, the mean square error:

[0033]

[0034] Among them, N is the number of neurons in the output layer of the simplified BP neural network; y it and are the true value and the predicted value of the historical measurement data of the distribution network respectively. The BP neural network based on the simplified power flow equation is trained by a supervised training method as the final initial value prediction model.

[0035] Step Six: Distribution network state estimation The weighted least squares method of

[0036] min J(x) = (z - h(x)) T R -1 (z - h(x)) (12)

[0037] Among them, z is the measurement value vector of the distribution network; h(x) is the measurement function vector of the distribution network; R is the measurement error variance matrix, and the elements in R are the reciprocals of the variances of the measurement devices; J(x) represents the minimum value of the square difference between the measurement function of the distribution network and the measurement value vector. To obtain the distribution network state estimation The objective function shown in formula (12) is partially differentiated with respect to x and let Then there is:

[0038] H(x)R -1 [z - h(x)] = 0 (13)

[0039] Among them, H(x) is the Jacobian matrix of the measurement function h(x).

[0040] The nonlinear measurement function is expanded near the initial state point x 0 of the system operation by using the Taylor series. Ignoring the high-order terms of the second order and above, only the constant term and the first-order term are retained, and the following linearized equation is obtained:

[0041] h(x) ≈ h(x 0 ) + H(x 0 )△x (14)

[0042] Among them, △x = x (k+1) - x (k) , which is the difference between the state variables of two iterations, and k is the iteration number. Combining formulas (13) and (14), the following iterative equation set is obtained:

[0043] △x (k+1)

[0044] = G -1 (x (k) )H T (x (k) )R -1 [z - h(x(k) )]x (k+1)

[0045] = x (k) + Δx (k) (15)

[0046] G(x (k) ) = H T (x (k) )R -1 H(x (k) ) (16)

[0047] Substitute the initial state point x output by the initial value prediction model obtained after training in step five 0 into formula (15) for calculation, taking the reference voltage modulus as 10 -6 ~10 -4 , when , calculate the current operating state of the distribution network, ε a is the set threshold value.

[0048] The present invention has the following beneficial effects:

[0049] This method prunes the neural network according to the distribution network topology, reduces the training parameters of the neural network, and reduces the computational amount. Since a three-layer BP neural network can theoretically fit any polynomial function, part of the parameters that do not need to be trained are pruned from the second layer to achieve the separation of voltage phase angle and amplitude; adding PMU to the neural network can further reduce the training parameters. Therefore, compared with the traditional fully connected BP neural network, the parameters required for its training are fewer, and its training time is shorter. Applying the initial value obtained from the neural network in this method to the Gauss-Newton method can improve the convergence of the Gauss-Newton method, and thus improve the accuracy of distribution network state estimation. Description of the Drawings

[0050] Figure 1 is the flow chart of distribution network state estimation based on a simplified power flow neural network.

[0051] Figure 2 is the schematic diagram of network segmentation based on the PMU position.

[0052] Figure 3 is the neural network based on the simplified power flow.

[0053] Figure 4 is the voltage amplitude training time and error curve of network training in the embodiment.

[0054] Figure 5 is the training time and error curve of the voltage phasor of network training in the embodiment.

[0055] Figure 6Initial value calculation results of different methods in the embodiments.

[0056] Figure 7 State estimation results of different methods in the embodiments. Specific implementation manners

[0057] The following combines the accompanying drawings and introduces the distribution network state estimation process based on this method according to the standard example of IEEE 33 nodes.

[0058] As Figure 1 shown, the distribution network state estimation method based on the simplified power flow neural network includes offline training and online application. The specific steps are as follows:

[0059] Step 1. Data collection

[0060] s1.1. Extract the loads of each node in the distribution network at different times according to the daily load curve in the historical database and make them into a data set.

[0061] s1.2. Select the total load data of 180 days in a certain area. Considering the spatio-temporal correlation of load changes, for the measurement data of 24 hours a day, each hour is used as a sample. Since the AMI measurement device can obtain 4 sets of sampling data per hour, and the AMI measurement records the injected active power and reactive power of the node, thus sample data with a dimension of 4320×8 can be obtained.

[0062] s1.3. Substitute the data obtained in s1.2 into the case33bw() power flow calculation program in Matpower to obtain the accurate network electrical quantities of the IEEE 33-node distribution network. Correspond the made data set with the accurate distribution network electrical parameters obtained through power flow calculation one by one to obtain a labeled data set, where the input data is the network electrical quantities obtained by the measurement device, and the label data is the network electrical quantities obtained through power flow calculation. The label data is regarded as accurate and error-free data.

[0063] s1.4. Since there are errors in the measurement device that follow a Gaussian distribution, the input data will not be completely accurate. Therefore, a Gaussian distribution with a mean of 0 and a variance of 0.001 is superimposed on the input data set obtained in s1.3 to make the measurement error "inaccurate" and simulate the measured quantities in the distribution network. Finally, a data set for training the BP neural network based on the simplified power flow equation is obtained.

[0064] Step 2. Network training

[0065] s2.1. Use Pytorch to read the data in the data set obtained in s1.4, and correspond the input quantity X and the label y therein to form a complete data set with one-to-one correspondence between input and output. Set 80% of them as training samples and the remaining 20% as test samples.

[0066] S2.2. Establish a BP neural network. For the IEEE 33 - node system, there are 33×2 state variables, including the voltage and amplitude of the reference node. Among them, the training parameters of the input layer are not simplified. There are 240 neurons in the hidden layer. Therefore, for a general BP neural network, the number of training parameters in the second layer is 240×33×2; according to this method, the network is pruned, and the number of training parameters in the second layer is simplified to 120×33×2. Compared with before pruning, the training parameters are reduced by half. Use Pytorch to write the neural network based on the simplified power flow as follows Figure 3 shown. Set the neural network model parameters and the parameters during training as shown in the following table:

[0067]

[0068]

[0069] S2.3. According to the above data loading, neural network model and training parameter settings, train this neural network. As shown in Figure 4 , Figure 5 shown, under the same epoch, the network after pruning by this method has fewer training parameters and shorter training time. After training, save this neural network for online calculation applications of state estimation.

[0070] Step Three: Online Application

[0071] S3.1. Save and load the neural network trained in S2.3. Input a real - time measurement data to obtain the initial value required for the distribution network state estimation as shown in Figure 6 shown.

[0072] S3.2. Calculate the node admittance matrix of the IEEE 33 - node distribution network, then set the initial value of the Gauss - Newton method according to the result of S3.1, and calculate the measurement matrix H according to the initial value:

[0073] h(x)≈h(x 0 )+H(x 0 )△x (17)

[0074] Therefore, the measurement matrix H is the Jacobian matrix of h(·), and the matrix elements are:

[0075]

[0076] Substitute the initial value of the network output into formula (17) to get h(x 0 ), and then according to:

[0077] △x (k+1)

[0078] =G-1 (x (k) )H T (x (k) )R -1 [z - h(x (k) )]x (k+1)

[0079] = x (k) + △x (k) (19)

[0080] G(x (k) ) = H T (x (k) )R -1 H(x (k) ) (20)

[0081] The state variables of the distribution network are obtained through iterative calculation.

[0082] S3.3. Perform iterative calculation according to the method in S3.2 to obtain the result as shown in Figure 7 . Since the initial value predicted by the neural network is closer to the actual value, the estimated value of the state variables of the distribution network is also closer to the true value, and the number of its iterations is the same as that of the fully connected neural network, which is 2 times. While directly setting the initial value to 1∠0° according to the traditional method requires 3 iterations. Therefore, the initial value can well reduce the number of iterations and time in the calculation process, and can reduce the possibility of non-convergence.

Claims

1. Method for calculating initial value of distribution network state estimation based on simplified power flow neural network, Characterized in that: This method specifically includes the following steps: Step 1: Establish a BP neural network, including an input layer, a hidden layer, and an output layer; among them, the number of neurons in the input layer is equal to the number of measurements in the distribution network, and the number of neurons in the output layer is equal to the number of state variables in the distribution network; Step 2: For a power system with n nodes, its AC power flow in polar coordinates is expressed as: Among them, P i and Q i are the active power and reactive power of node i respectively; V i and V j represent the voltage amplitudes of nodes i and j respectively, θ ij is the phase angle difference between node i and node j, i, j = 1, 2, …, n; G ij +jB ij = Y ij , Y ij represents the element in the node admittance matrix Y, G ij and B ij represent the real part and the imaginary part of the element in the i-th row and j-th column of the node admittance matrix Y respectively; According to the values of the node voltage amplitude and voltage phase angle in the power system, there is: where b ij and g ij are the conductance and susceptance between nodes i and j, respectively. Substitute Equation (2) into Equation (1) to decouple the voltage magnitude and voltage phase angle according to the active power and reactive power: Converted to matrix representation as: Step 3. When the formula (5) has a solution, that is when it is invertible, there is According to the node voltage amplitude, is transformed into: Substituting formula (7) into formula (6) gives: Let Decompose the voltage amplitude V and the voltage phase angle θ into: According to formula (9), it can be seen that the voltage phase angle θ and voltage amplitude V can be decomposed into two parts. Therefore, half of the neurons in the hidden layer are fully connected to the neurons of the node voltage amplitude in the output layer; the other half of the neurons are fully connected to the neurons of the node voltage phase angle in the output layer to obtain a simplified BP neural network; Step 4: For a distribution network equipped with L PMUs, divide it into L - 1 parts according to the positions of the PMUs: Among them, Y' 11 ,Y' 22 ,...,Y' LL are the coefficient admittance matrices of each part after being segmented by the PMU, respectively. Y' 12 ,Y' 21 ,Y' 1L ,Y' L1 ,Y' 2L ,Y' L2 are the coefficient admittance matrices between different parts of the PMU. Since there are only very few connection relationships at the PMU connection nodes in the radial distribution network, therefore, Y' 12 ,Y' 21 ,Y' 1L ,Y' L1 ,Y' 2L ,Y' L2 can be considered as a zero matrix; According to the topological structure of the segmented distribution network, divide the simplified BP neural network in Step 3 into multiple groups of neural networks to obtain a BP neural network based on the simplified power flow equation; Step 5: Set the loss function as MSE loss, and use a supervised training method to train the BP neural network based on the simplified power flow equation as the final initial value prediction model; Step 6: Input the true measurements on the distribution network into the initial value prediction model obtained after training in Step 5, and use the result output by the model as the initial value of the Gauss-Newton method to solve the operating state of the distribution network, and perform distribution network state estimation The weighted least squares method of min J(x) = (z - h(x)) T R -1 (z - h(x)) (12) where \(z\) is the measurement value vector of the distribution network; \(h(x)\) is the measurement function vector of the distribution network; \(R\) is the measurement error variance matrix, and the elements in \(R\) are the reciprocals of the variances of the measurement devices; \(J(x)\) represents the minimum value of the square difference between the measurement function of the distribution network and the measurement value vector; to obtain the state estimation of the distribution network Take the partial derivative of the objective function shown in formula (12) with respect to \(x\) and let Then we have: H(x)R -1 [z - h(x)] = 0 (13) where H(x) is the Jacobian matrix of the measurement function h(x); Expand the non - linear measurement function at the initial state point \(x\) of the system operation using the Taylor series, neglect the higher - order terms of the second - order and above, and only retain the constant term and the first - order term to obtain the following linearized equation: 0 Nearby, ignoring the higher - order terms of the second - order and above, only retaining the constant term and the first - order term, the following linearized equation is obtained: h(x)≈h(x 0 )+H(x 0 )△x(14)where △x=x (k+1) -x (k) , is the difference between the two iteration state variables, k is the number of iterations; combining formulas (13) and (14), we get the following iterative equations: △x (k+1) = G -1 (x (k) )H T (x (k) )R -1 [z - h(x (k) )]x (k+1) = x (k) + Δx (k) (15) G(x (k) ) = H T (x (k) )R -1 H(x (k) ) (16) Substitute the initial state point x output by the network 0 into formula (15) for calculation, and take the reference voltage modulus as 10 -6 ~10 -4 , when , calculate the current operating state of the distribution network, ε a is the set threshold value.

2. The method for calculating the initial value of the distribution network state estimation based on the simplified power flow neural network according to claim 1, Characterized in that: The MSE loss is the mean of the sum of the squares of the errors of the corresponding points between the predicted data and the original data: where N is the number of neurons in the output layer of the simplified BP neural network; y it , are the true value and the predicted value of the historical measurement data of the distribution network, respectively.

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