CN116418000A

CN116418000A - Bayesian state estimation method for unobservable distribution network based on embedded tide neural network

Info

Publication number: CN116418000A
Application number: CN202211343951.XA
Authority: CN
Inventors: 梁栋; 刘啸宇
Original assignee: Hebei University of Technology
Current assignee: Hebei University of Technology
Priority date: 2022-10-31
Filing date: 2022-10-31
Publication date: 2023-07-11

Abstract

The invention relates to a Bayesian state estimation method of an unobservable distribution network based on an embedded power flow neural network, which comprises the following steps of: step 1, learning two-dimensional Gaussian mixture probability distribution of active power and reactive power injected into each node; step 2, sampling and obtaining sufficient node injection power data from the GMM to obtain a large number of injection power samples; step 3, obtaining mass data samples for neural network training; step 4, establishing a Bayesian state estimation model of the unobservable power distribution network based on the PFENN, and obtaining a consistent solution meeting the power flow constraint of the power grid operation by superposing a physical loss penalty term of the power flow in a loss function to perform neural network training; and 5, inputting real-time measurement into the neural network model trained in the off-line stage, and rapidly obtaining a voltage estimation result through forward calculation. The method and the device can solve the problem that the existing power distribution network state estimation method is low in accuracy under the condition of insufficient real-time measurement.

Description

Bayesian state estimation method for unobservable distribution network based on embedded tide neural network

Technical Field

The invention belongs to the technical field of situation awareness of power distribution networks, relates to a Bayesian state estimation method of a power distribution network, and particularly relates to a Bayesian state estimation method of an unobservable power distribution network based on an embedded power flow neural network.

Background

The high proportion of renewable energy grid connection becomes a necessary development trend and important characteristic of a future power system. However, the continuous improvement of the permeability of the distributed generation (distributed generation, DG) and the continuous increase of the holding capacity of the electric automobile make the operation mode and the dynamic behavior of the power distribution network more complex, and the power distribution network has problems such as increased voltage level, increased short-circuit current, reduced power supply reliability, deteriorated power quality and the like, so that the situation awareness level needs to be improved, and the safe, reliable and economic operation of the power distribution network is ensured.

The state estimation is used for acquiring the complete, reliable and consistent running state of the whole grid, and is an important tool for realizing the sensing of the running situation of the power grid and the improvement of the toughness. In recent years, an advanced measurement system (advanced measurement infrastructure, AMI) with a smart meter as a core realizes accurate acquisition of electricity consumption at a user node level; at the same time, miniaturized and low-cost miniature synchronous phasor measurement units (micro-phasor measurement unit, mu PMU) gradually replace the traditional SCADA measurement to obtain the favor of power grid planning operators. However, due to the time delay problem of AMI measurement, the acquisition period of even important users can reach 15/30 minutes; the power distribution network is large in scale, mu PMU can be configured at limited key nodes, and the whole network observable conditions required by real-time situation awareness cannot be provided.

The neural network has strong fitting capability, can fully approximate to any function, and scholars at home and abroad develop various pseudo measurement modeling and state estimation method researches based on the neural network from different angles. The existing literature feeds back the state estimation result to a machine learning module for estimating the node load to form a closed-loop information flow, and the performance of both state estimation and load estimation is improved. The prior literature models the load pseudo measurement by adopting a neural network firstly based on annual historical data, and models the sample error by using a Gaussian mixture model (gaussian mixture model, GMM); at the state estimation moment, the real-time measurement is input into a trained neural network to obtain the high-precision injection pseudo measurement, and the weight is set according to the distance between the pseudo measurement value and the expected distance of each Gaussian distribution component in the GMM, so that the weighted least square (weighted least squares, WLS) estimation is performed. As a non-statistical estimation method, WLS estimation is equivalent to maximum likelihood estimation when measurement errors follow Gaussian distribution, and has excellent characteristics of optimal consistency, unbiased property and minimum variance. However, for an unobservable power distribution system with insufficient real-time measurement, the WLS estimation cannot be directly applied, and the estimation accuracy of the pseudo-measurement generation-WLS estimation two-stage method is seriously dependent on the accuracy and weight of the pseudo-measurement, so that the excellent characteristics of the WLS cannot be maintained.

In recent years, attention has been paid to bayesian estimation methods such as maximum a posteriori estimation and minimum mean square error (minimum mean square error, MMSE) estimation. The prior literature aims at minimizing the mean square error of a state variable, proposes a Bayesian state estimation method of an unobservable power distribution network based on deep learning, and adopts a neural network to carry out parameterized approximation on the condition expectation of the state variable. However, the neural network black box type working method makes the result poor in interpretation and generalization performance, and the inference may not meet the known physical conditions. A neural network (physics-informed neural network, PINN) embedded with physical knowledge may guide model learning through the physical knowledge to obtain a solution consistent with the physical knowledge. The prior art prunes unnecessary neural network connections based on physical knowledge to prevent overfitting, or estimates system status via the PINN when the system fails suddenly or is missing in measurement but is not observable based on historical time series data and real-time measured time-space information.

No prior art patent document, which is the same as or similar to the present invention, was found after searching.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, and provides an unobservable power distribution network Bayesian state estimation method based on an embedded power flow neural network, which can solve the problem of lower precision of the conventional power distribution network state estimation method under the condition of insufficient real-time measurement.

The invention solves the practical problems by adopting the following technical scheme:

a Bayesian state estimation method of an unobservable power distribution network based on an embedded power flow neural network comprises the following steps:

step 1, based on limited AMI historical data, carrying out statistical modeling on load and DG output, and learning two-dimensional Gaussian mixture probability distribution of active power and reactive power injected into each node;

step 2, performing Monte Carlo sampling on the learned two-dimensional Gaussian mixture probability distribution of active power and reactive power of each node injection, and sampling to obtain sufficient node injection power data from the GMM to obtain a large number of injection power samples;

step 3, performing conventional power flow calculation on each injected power sample based on element parameters and the current network topology to obtain mass data samples for neural network training;

step 4, taking the minimized state estimation error as a target, using the mass data sample obtained in the step 3, establishing a Bayesian state estimation model of the unobservable power distribution network based on the PFENN, and obtaining a consistent solution meeting the power grid operation power flow constraint by superposing a power flow physical loss penalty term in a loss function to perform neural network training;

and 5, inputting real-time measurement into the neural network model trained in the off-line stage, and rapidly obtaining a voltage estimation result through forward calculation.

Moreover, the specific steps of the step 1 include:

(1) Let GMM of the polynary random variable x be:

wherein: k is the number of the components of the multi-element Gaussian distribution; f (x|mu) _i ,Σ _i ) A probability density function for the ith multivariate gaussian distribution component; mu (mu) _i ,Σ _i The expected vector and covariance matrix of the ith multivariate Gaussian distribution component; w (w) _i The weight of the ith multivariate Gaussian distribution component is satisfied with w ₁ +w ₂ +L+w _K ＝1。

(2) And establishing two-dimensional GMM of active and reactive load for each node, solving the weight, expectation and covariance matrix of each multi-element Gaussian distribution component by adopting an expectation maximization algorithm based on historical active and reactive load data, and determining the component quantity of each GMM by taking a Bayesian information criterion as a criterion.

Moreover, the specific steps of the step 2 include:

performing Monte Carlo sampling on two-dimensional Gaussian mixture probability distribution of active power and reactive power injected into each node learned based on limited data in the step 1, performing random sampling from a known probability density function to realize mathematical simulation of a problem to be solved, and acquiring sufficient node injection power data to obtain a large number of injection power samples;

the specific method of the step 3 is as follows:

and (3) under the condition of knowing element parameters and current topology, taking the samples extracted in the step (2) as node injection power to perform load flow calculation, and obtaining the running states of a plurality of time sections of the whole network.

Moreover, the specific steps of the step 4 include:

(1) Structural design of neural network

The method comprises the steps of adopting a fully-connected neural network, and calculating an output result by forward propagation based on training data and weight parameters, wherein the fully-connected neural network consists of an input layer, an output layer and a plurality of hidden layers; the back propagation calculates the gradient of the loss function to each parameter through the derivative chain rule, and the parameter is updated according to the gradient. The minimum loss function is used as a target, and the network parameters are optimized through forward and reverse repeated iteration;

(2) Establishing a loss function of the neural network:

the mean absolute error MAE is used as a loss function to approximate the neural network of the MMAE estimator, and the formula is as follows:

wherein: n is the number of training samples; x is a state truth (label) vector;

is a state estimation value vector.

The physical loss function expression is:

wherein:

based on the state estimation result ∈>

The calculated node injection complex power vector, node injection active power vector, node injection reactive power vector, node complex voltage vector and node injection complex current vector; p, Q, U, I are true value vectors of node injection active power, node injection reactive power, node complex voltage and node injection complex current respectively; y is the node admittance matrix; * Is complex conjugate operation; e is the vector multiplication by element.

After the physical loss function is considered, the loss function of the neural network is as follows:

loss＝α·loss _physics +(1-α)·loss _MAE (4)

wherein: alpha is a super parameter for adjusting the weight of two loss, and alpha is more than or equal to 0 and less than or equal to 1.

(3) Optimizing the super parameters based on a BOHB algorithm to further obtain a neural network model after training;

(1) taking the training round number of each group of super parameters as calculation resources, and supposing that each 1 calculation resource represents 50 training rounds; setting the maximum allocation resource as bmax=9 and the minimum allocation resource as bmin=1, wherein the number of each evaluation subset which can enter the next round of evaluation is 1/eta;

(2) allocating a small amount of computing resources to different parameter combinations, and gradually increasing computation for the parameter combinations which are excellent in performance; and the model trained by all the parameter combinations is evaluated by using a verification set, the evaluation result is transmitted to a Bayesian optimizer, and the next group of parameters is continuously searched for further evaluation according to the known result.

The specific method of the step 5 is as follows:

and (3) acquiring partial real-time measurement data by using a limited real-time measurement device as input of the PFENN model trained in the step (4), and rapidly acquiring the whole network state by forward calculation of the model.

The invention has the advantages and beneficial effects that:

1. aiming at the problem of low accuracy of the existing power distribution network state estimation method under the condition of insufficient real-time measurement, the invention provides an unobservable power distribution network Bayesian state estimation method based on a power flow-embedded neural network (PFENN) embedded network. Firstly, based on limited historical electricity utilization data, learning two-dimensional Gaussian mixture probability distribution of active power and reactive power injection, and accordingly, sampling Monte Carlo to obtain abundant samples for training a neural network; secondly, a Bayesian state estimation model based on PFENN is built with the minimum state estimation error as a target, and a physical consistent solution meeting the operation constraint of the power grid is obtained by integrating a tide physical loss penalty term into a loss function; furthermore, the super parameters of the neural network model are optimized through a BOHB method, so that the problems of long calculation chain, slow training and difficult parameter adjustment caused by large data volume and power flow embedding are solved. The test result shows that the method has higher estimation precision compared with the existing power distribution network state estimation method based on pseudo measurement and the Bayesian estimation method without current embedding.

2. Based on limited historical electricity utilization data, the two-dimensional Gaussian mixture probability distribution of active power and reactive power is learned and injected, and Monte Carlo sampling is carried out according to the two-dimensional Gaussian mixture probability distribution to obtain abundant samples for training a neural network. The model is fully trained. Because the power distribution network is directly oriented to power users, the load of the power distribution network often has asymmetric and multimodal characteristics, and compared with single Gaussian distribution fitting and only using original data, the estimation precision of a model can be remarkably improved by adopting a GMM extended training set.

3. According to the invention, the Bayesian state estimation model based on the embedded power flow neural network is built with the aim of minimizing the state estimation error, and the physical consistent solution meeting the power grid operation constraint can be obtained by integrating the power flow physical loss penalty term into the loss function, so that the method is suitable for unobservable power distribution network state estimation with insufficient measurement. By embedding the tide into the neural network, the interpretability and generalization capability of the Bayesian state estimation model are improved, and the result accords with the constraint of physical conditions, so that the estimation precision can be further improved.

4. According to the invention, the super parameters of the neural network model are optimized by the BOHB method which combines the advantages of the Bayesian optimization and the hyper band method, so that the problems of long calculation chain, slow training and difficult parameter adjustment caused by large data volume and power flow embedding are solved.

5. Compared with the existing power distribution network state estimation method based on pseudo measurement and the existing Bayesian estimation method without the embedding of the tide flow, the method provided by the invention has higher estimation precision.

Drawings

FIG. 1 is a process flow diagram of a PFENN-based Bayesian state estimation method for an unobservable power distribution network of the present invention;

FIG. 2 is a two-dimensional probability density chart of actual active and reactive loads of a certain area provided by an embodiment of the invention;

fig. 3 is a schematic structural diagram of an embedded power flow neural network according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of a BOHB algorithm provided by an embodiment of the present invention;

FIG. 5 is a schematic diagram of a measurement configuration of a 33 node power distribution system according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of an optimized neural network according to an embodiment of the present invention;

FIG. 7 (a) is a phase angle absolute error frequency histogram of state estimation provided by an embodiment of the present invention;

FIG. 7 (b) is a histogram of absolute error frequency of the state estimation amplitude provided by an embodiment of the present invention;

FIG. 8 (a) is a graph comparing voltage phase angle estimation curves of node 5 obtained by four methods according to the embodiment of the present invention;

FIG. 8 (b) is a graph comparing voltage amplitude estimation curves of node 5 obtained by four methods according to an embodiment of the present invention;

FIG. 9 (a) is a graph comparing the estimated APE curves of the voltage phase angle of the node 5 obtained by four methods according to the embodiment of the present invention;

fig. 9 (b) is a comparison graph of node 5 voltage amplitude estimation APE curves obtained by four methods according to an embodiment of the present invention;

FIG. 10 (a) is a graph comparing voltage phase angle estimation curves of node 19 under GMM sampling and non-sampling according to an embodiment of the present invention;

FIG. 10 (b) is a graph comparing voltage amplitude estimation curves of node 19 under GMM sampling and non-sampling according to an embodiment of the present invention;

FIG. 11 (a) is a graph comparing the estimated APE curves of the voltage phase angles of the nodes 19 under the sampling and non-sampling of the GMM according to the embodiment of the present invention;

FIG. 11 (b) is a graph comparing the estimated APE curves of the voltage amplitude of node 19 under the sampling and non-sampling of the GMM according to the embodiment of the present invention;

FIG. 12 (a) is a graph showing the comparison of the phase angle MSE of all node voltages under four test schemes according to the embodiment of the present invention;

FIG. 12 (b) is a graph showing comparison of MSE values of all node voltages under four test schemes according to an embodiment of the present invention;

FIG. 13 (a) is a schematic diagram showing a change situation of a loss function of a training process in a BOHB optimization process according to an embodiment of the present invention;

FIG. 13 (b) is a schematic representation of model input of different parameters in a verification set in the BOHB optimization process according to the embodiment of the invention;

FIG. 14 (a) is a graph comparing node 10 voltage phase angle estimation curves obtained by two super-parameter optimization methods, namely BOHB and Bayesian optimization, provided by the embodiment of the invention;

FIG. 14 (b) is a graph comparing voltage amplitude estimation curves of the node 10 obtained by two super-parameter optimization methods, namely BOHB and Bayesian optimization, according to the embodiment of the present invention;

FIG. 15 (a) is a comparison chart of node 10 voltage phase angle estimation MAPE obtained by two super-parameter optimization methods, namely BOHB and Bayesian optimization, provided by the embodiment of the invention;

FIG. 15 (b) is a comparison chart of the node 10 voltage amplitude estimation MAPE obtained by two super-parameter optimization methods, namely BOHB and Bayesian optimization, according to an embodiment of the present invention;

FIG. 16 (a) is a comparison chart of the phase angle estimation MAE of two super-parameter optimization methods, BOHB and Bayesian optimization, provided by the embodiment of the invention;

FIG. 16 (b) is a comparison chart of amplitude estimation MAE of two super-parameter optimization methods, BOHB and Bayesian optimization, provided by the embodiment of the invention;

Detailed Description

Embodiments of the invention are described in further detail below with reference to the attached drawing figures:

an unobservable power distribution network Bayesian state estimation method based on an embedded power flow neural network, as shown in figure 1, comprises the following steps:

the specific steps of the step 1 comprise:

(1) Let GMM of the polynary random variable x be:

In this embodiment, the working principle of the step 1 is as follows:

sufficient training sample data is a precondition for successful application of the neural network based state estimation method. However, neural network parameters are numerous, the amount of historical data may not meet training needs, and it is difficult to extract timing features on a finer time scale based on discrete historical data sampled at equal intervals. Therefore, a large number of simulation samples need to be acquired to participate in training through probability distribution learning and Monte Carlo sampling. The parameter model and the non-parameter model are the most common two types of probability modeling methods, wherein the former thinking is to presuppose that random variables obey a certain probability density distribution, and then parameter estimation is carried out on the probability model according to historical data. The load data of the large regional power grid can be approximately considered to follow Gaussian distribution, however, the power distribution network is directly oriented to power users, the load of the power distribution network often has asymmetric and multimodal characteristics, and the fitting precision is low by adopting single Gaussian distribution.

The GMM describes probability distribution characteristics of non-gaussian random variables through weighted linear combination of a plurality of gaussian distributions, and can theoretically fit any type of distribution, so that the GMM is suitable for solving the problem that a data set contains a plurality of different distributions. Based on the actual load data of a certain city distribution network area for one month, the two-dimensional GMM probability density of the active and reactive loads is drawn as shown in figure 2. As can be seen from fig. 2, the active and reactive loads exhibit a more pronounced correlation and multimodal character.

in this embodiment, the monte carlo simulation is a calculation method based on a probability and statistical theory method, which is also called a random sampling or statistical test method, and the basic principle is to convert the complex problem to be solved into a simple repeated test. Firstly, the statistical modeling of the load and the DG output in the step 1 is completed, then the random sampling is carried out from the known probability density function to realize the mathematical simulation of the problem to be solved, and finally the estimated quantity to be solved is established. According to the law of large numbers, the estimator will tend to be a true value when the sample size of the random sample is large enough.

the specific method of the step 3 is as follows:

the specific steps of the step 4 include:

(1) Structural design of neural network

As shown in fig. 3, a fully connected neural network (fully connected neural network, FCNN) is adopted, and the fully connected neural network consists of an input layer, an output layer and a plurality of hidden layers, and forward propagation calculates an output result based on training data and weight parameters; the back propagation calculates the gradient of the loss function to each parameter through the derivative chain rule, and the parameter is updated according to the gradient. And (3) aiming at minimizing the loss function, and performing forward and reverse iteration to optimize the network parameters.

In this embodiment, in terms of the structure of the neural network, since the real-time state estimation method provided by the present invention only relies on real-time measurement at the current moment, the input dimension is small, and the cyclic neural network (residual neural network, RNN) and the convolutional neural network are not suitable.

(2) Establishing a loss function of the neural network:

the Mean Absolute Error (MAE) is used as a loss function to approximate the neural network of the MMAE estimator, and the formula is as follows:

is a state estimation value vector.

Under the condition of abundant data, the neural network model driven by pure data can reach high precision, but the working method of the neural network black box type leads the interpretation of the result to be weaker and the generalization performance to be poor, and the inference may not conform to the known physical conditions. Therefore, on the basis of the MAE loss function, the power system load flow equation is embedded, and the physical loss function is constructed based on the degree of violation of the load flow equation by the neural network output vector, so that the neural network output vector also participates in the training process, and the feasible space of the neural network weight parameter is limited by taking the neural network output vector as a punishment term, so that the output result is ensured to accord with the load flow physical constraint. The physical loss function expression is:

wherein:

based on the state estimation result ∈>

The calculated node injection complex power vector, node injection active power vector, node injection reactive power vector, node complex voltage vector and node injection complex current vector; p, Q, U, I true value directions of active power injected into the node, reactive power injected into the node, complex voltage and complex current injected into the nodeAn amount of; y is the node admittance matrix; * Is complex conjugate operation; e is the vector multiplication by element.

loss＝α·loss _physics +(1-α)·loss _MAE (4)

(3) And optimizing the super parameters based on the BOHB algorithm to further obtain the trained neural network model.

(2) a small amount of computing resources are allocated to different combinations of parameters, and the computation is incrementally increased for combinations of parameters where the performance is excellent. And the model trained by all the parameter combinations is evaluated by using a verification set, the evaluation result is transmitted to a Bayesian optimizer, and the next group of parameters is continuously searched for further evaluation according to the known result.

In this embodiment, the result of the neural network is extremely sensitive to the selection of the super-parameters, so that the super-parameters such as the depth, width, learning rate, loss weight, etc. of the network are optimized, so that the estimation effect of the whole network is optimized. In various super-parametric optimization methods: the grid search method has huge calculation amount and is time-consuming and labor-consuming; random search methods are generally faster than grid search, however, the number of searches is unstable; bayesian optimization finds the optimal parameters by constructing posterior probabilities of black box functions. However, in the bayesian optimization training process, if the parameter selection is not good at the beginning, the training is still waited, so that the resource and time are wasted. In order to rapidly complete the optimization task, the invention adopts a BOHB (Bayesian optimization and Hyperband) super-parameter optimization strategy which combines the advantages of the Bayesian optimization and the hyper-band method on the basis of Bayesian optimization.

The core idea of the BOHB method is shown in fig. 4, where the number of training rounds per set of hyper-parameters is taken as the computing resource, and it is assumed that each 1 computing resource represents 50 training rounds. Let bmax=9 assigned maximum resources and bmin=1 assigned minimum, the number of each evaluation subset that can go to the next round of evaluation is 1/η. First, a small amount of computing resources are allocated to different parameter combinations, and computation is gradually increased for the parameter combinations in which the performance is excellent. And the model trained by all the parameter combinations is evaluated by using a verification set, the evaluation result is transmitted to a Bayesian optimizer, and the next group of parameters is continuously searched for further evaluation according to the known result.

Compared with Bayesian optimization, the BOHB method remarkably improves the calculation speed while keeping the Bayesian optimization precision as much as possible, and the precision loss is derived from: the error of the truncated parameter combination drops slowly in the initial stage, but the error has a certain probability of being converged to a smaller value.

The specific method in the step 5 is as follows:

The innovation of the invention is that:

the invention provides a Bayesian state estimation method of an unobservable power distribution network based on an embedded power flow neural network. Firstly, based on historical electricity utilization data of each load node, learning two-dimensional Gaussian mixture probability distribution of active power and reactive power injection, and accordingly, carrying out Monte Carlo sampling and tide calculation to obtain rich samples for neural network training; secondly, with the minimum state estimation error and the power flow equation out-of-limit as targets, a power distribution network Bayesian state estimation model based on an embedded power flow neural network is established, and a consistent solution meeting the power grid operation constraint is obtained by integrating a power flow physical loss penalty term into a loss function; furthermore, the super parameters of the neural network model are optimized by a BOHB method, so that the problems of long calculation chain, slow training and difficult parameter adjustment caused by large data volume and power flow embedding are solved; finally, the actual data and the test result of the 33-node power distribution network calculation example show that the method has higher estimation precision compared with a state estimation method based on pseudo measurement and a Bayesian estimation method without embedded moisture.

The method is used for solving the problem of estimating the state of the local observable distribution network under the condition of insufficient measurement, researching the cut-in from the perspective of the neural network, and avoiding the defects that the estimation precision is lower or even can not be realized when the measurement is insufficient in the traditional analytic solving method; secondly, the result of the neural network model driven by data is weak in interpretation and poor in generalization performance, and the inference of the result possibly does not accord with the known physical conditions; aiming at the problems of large data size, long calculation chain length, slow training and difficult parameter adjustment in the process of parameter adjustment of the neural network, the invention optimizes the super parameters of the neural network model by the BOHB method, thereby saving time and improving efficiency under the condition of ensuring the precision. The test result shows that the method has higher estimation precision compared with the existing power distribution network state estimation method based on pseudo measurement and the Bayesian estimation method without current embedding.

The working principle of the invention is as follows:

the invention discloses a Bayesian state estimation method of an unobservable power distribution network based on an embedded power flow neural network, which comprises the following steps of: s1, carrying out statistical modeling on load and DG output based on limited AMI historical data, and learning two-dimensional Gaussian mixture probability distribution of active power and reactive power injected into each node; s2, performing Monte Carlo sampling on the learned two-dimensional Gaussian mixture probability distribution of active power and reactive power of each node injection, and sampling to obtain sufficient node injection power data from the GMM to obtain a large number of injection power samples; s3, performing conventional power flow calculation on each injected power sample based on element parameters and the current network topology to obtain mass data samples for neural network training; s4, taking the minimized state estimation error as a target, using the mass data samples obtained in the step S3, establishing a Bayesian state estimation model of the unobservable power distribution network based on the PFENN, and obtaining a consistent solution meeting the power grid operation power flow constraint by superposing a power flow physical loss penalty term in a loss function to perform neural network training; s5, inputting real-time measurement into the neural network model trained in the off-line stage, and rapidly obtaining a voltage estimation result through forward calculation.

And when the two-dimensional Gaussian mixture probability distribution of active power and reactive power injected by each node is learned in the step S1, the weight, the expectation and the covariance matrix of each multi-element Gaussian distribution component are solved by adopting an expectation maximization algorithm, and the component quantity of each GMM is determined by taking a Bayesian information criterion as a criterion.

And S2, acquiring sufficient node injection power data after learning the two-dimensional Gaussian mixture probability distribution from the actual operation data with limited data quantity, and obtaining a large number of injection power samples.

And step S3, carrying out load flow calculation by taking the samples extracted in the step S2 as node injection power, and obtaining the running states of a plurality of time sections of the whole network.

The step S4 adopts a fully connected neural network (fully connected neural network, FCNN) which consists of an input layer, an output layer and a plurality of hidden layers; on the basis of the MAE loss function, embedding a power system power flow equation, constructing a physical loss function based on the degree of violation of the power flow equation by the neural network output vector, so that the physical loss function also participates in the training process, and limiting the feasible space of the neural network weight parameter by taking the physical loss function as a penalty term to ensure that an output result accords with the power flow physical constraint; and optimizing the super parameters of the neural network based on the BOHB algorithm, so as to obtain the neural network model after training.

And S5, acquiring partial real-time measurement data by using a limited real-time measurement device as input of the PFENN model trained in the step S4, and rapidly acquiring the whole network state by forward calculation of the model.

The invention is further illustrated by the following examples:

1. simulation configuration

As shown in fig. 5, the proposed state estimation method was subjected to an example test using a 33-node power distribution system.

Assuming that the component parameters and the network topology are known and kept unchanged, the substation branch 1-2 is configured with real-time active and reactive power measurement, and six branches 1-2, 2-3, 8-9, 13-14, 19-20 and 28-29 are selected to be configured with branch current amplitude and phase angle measurement. Training the neural network by using actual operation data of a plurality of distribution transformer areas of a certain city in China for three months, wherein the time interval for data acquisition is 15 minutes, and the total time is 8832, and the data of each transformer area are randomly distributed to nodes of a 33-node system. The first 7000 pieces of data were selected for statistical modeling and neural network training, 7001 to 8000 pieces of data were used for verification, 8001 to 8832 pieces of data were used for testing.

In order not to leak the test set, the historical data for two-dimensional GMM modeling comes only from the training set. And generating 50000 node active and reactive load samples for the GMM model through Monte Carlo sampling, and performing power flow calculation by using MATIPOWER to generate a measurement-state sample, wherein Gaussian random disturbance with standard deviation of 0.03 is added to a measurement true value obtained by power flow calculation so as to improve the robustness of the neural network. In order to prevent other input data from being disabled due to overlarge input values when the dimensions are different, the data is scaled to the [0,1] interval by using a maximum value-minimum value normalization method in a data preprocessing stage.

All tests were implemented using the PyTorch framework programming, and the width, depth, learning rate, and weight of the loss function of the full connection layer were automatically selected by the BOHB algorithm within the set search space. And searching 100 groups of parameters, performing verification on the verification set, and selecting the optimal parameters. The search space is shown in the following table:

table 1BOHB Algorithm hyper-parameter search space

The optimized neural network structure is shown in fig. 6, the input is the first switch active power, 32 current amplitudes, the first switch reactive power and 32 current phase angles, wherein the branch position without complex current is 0, and the output is the voltage amplitude and the phase angle of all unbalanced nodes. The activation function uses a LeakyReLU, the learning rate, the discarding rate and the loss function weight alpha are 0.000355, 0.494 and 0.719 respectively, the hidden layer is three layers, and 512 neurons are arranged in each layer.

2. Single distribution and GMM contrast test

Statistical modeling and sampling are respectively carried out on the original data by using single Gaussian distribution and GMM, then state estimation test is carried out on the test set data by the method provided by the invention, and the absolute error histograms of the estimation values of the phase angles and the amplitude values of the obtained voltages are shown in fig. 7 (a) and 7 (b). As can be seen, the error of the result using the two-dimensional GMM is more concentrated around 0, and the state estimation effect is better than that of a single gaussian distribution.

3. Different state estimation method contrast test

The following four methods were subjected to comparative tests:

1) pseudo-metrology+WLS estimation, after sampling by GMM, using FCNN to generate pseudo-metrology (WLS-FCNN): the input is the current real-time measurement; the false measurement weight is set by the inverse of the variance of the first 50 historical false measurement errors at the moment to be estimated.

2) pseudo-metrology+WLS estimation, pseudo-metrology (WLS-RNN+FCNN) is generated using RNN and FCNN hybrid neural networks: the input of the method is the first 50 historical data of the current moment and the current real-time measurement; the dummy measurement weight setting mode is the same as that of WLS-FCNN.

3) Bayesian state estimation (Bayes): after sampling by the GMM, performing state estimation by adopting FCNN, wherein the input is real-time measurement at the current moment, and the output is a system state without embedded tide.

4) The method (PINN-Bayes) of the invention: after sampling by the GMM, the state estimation is carried out by adopting the PFENN, the input is real-time measurement at the current moment, and the output is the system state.

The four state estimation methods are subjected to comparison test, voltage amplitude and phase angle estimation value curves of the node 5 obtained by the four methods are shown in fig. 8 (a) and 8 (b), absolute percentage error (absolute percentage error, APE) curves of the corresponding state estimation values are shown in fig. 9 (a) and 9 (b), and only the first 300 moments are selected for clarity of display.

As can be seen from the figure, compared with the last two bayesian estimation methods, the first two WLS estimation methods based on pseudo measurement have larger APE; compared with a Bayesian estimation method without the embedding of the tide flow, the method provided by the invention has higher estimation precision no matter the voltage amplitude value or the phase angle.

4. GMM sampling effect test

To verify the effect of using GMM rich training samples on estimation accuracy, the proposed method of the present invention was compared with the non-sampled method, the voltage amplitude and phase angle estimation curves of node 19 are shown in fig. 10 (a) and 10 (b), and the corresponding estimation APE curves are shown in fig. 11 (a) and 11 (b). The graph shows that the method is more accurate in the estimated values of the phase angle and the amplitude, and the effect of the GMM extended training set on the estimation effect of the lifting model is obvious.

In order to integrally show the influence of PFENN and GMM sampling in the method on the estimation effect, four schemes are subjected to comparison test: 1) Original data + no-stream embedding; 2) GMM sampling + no-tidal embedding; 3) Original data + tide embedding; 4) GMM sampling + power flow embedding. The MSE index for all node voltage magnitudes, phase angles on the test set for the four schemes is shown in fig. 12 (a) and 12 (b). It can be seen from the figure that the estimation accuracy can be remarkably improved by using the GMM rich training samples and embedding the power flow into the neural network.

5. Different super parameter optimization method contrast test

The section tests two super-parameter optimization methods, namely Bayesian optimization and BOHB. The BOHB optimization process is shown in fig. 13 (a) and fig. 13 (b), and it can be seen from the graph that as the number of training rounds increases, the value of the loss function is continuously reduced, but only the parameter combinations with better performance and smaller loss function on the verification set are allocated more computing resources, and training is continued. The voltage amplitude and phase angle estimated value curves of the node 10 under the two super-parameter optimization methods are shown in fig. 14 (a) and 14 (b), the corresponding estimated value APE curves are shown in fig. 15 (a) and 15 (b), and the MAE indexes of all node voltage amplitude and phase angle on the test set are shown in fig. 16 (a) and 16 (b). From the graph, the Bayesian optimized MAPE was 5.996 ×10 ^-4 M of BOHB methodAPE of 7.99X10 ^-4 . Although the Bayesian optimization accuracy is higher, the calculation time is longer, the same 100 groups of super-parameters are optimized, the Bayesian optimization takes 7h 18min56s, the BOHB method takes only 1h 49min 51s, and the time is about one fourth of the former.

It should be emphasized that the embodiments described herein are illustrative rather than limiting, and that this invention encompasses other embodiments which may be made by those skilled in the art based on the teachings herein and which fall within the scope of this invention.

Claims

1. A Bayesian state estimation method of an unobservable power distribution network based on an embedded power flow neural network is characterized by comprising the following steps of: the method comprises the following steps:

2. The method for estimating the Bayesian state of the unobservable power distribution network based on the embedded power flow neural network according to claim 1, wherein the method comprises the following steps of: the specific steps of the step 1 comprise:

(1) Let GMM of the polynary random variable x be:

wherein: k is the number of the components of the multi-element Gaussian distribution; f (x|mu) _i ,Σ _i ) A probability density function for the ith multivariate gaussian distribution component; mu (mu) _i ,Σ _i The expected vector and covariance matrix of the ith multivariate Gaussian distribution component; w (w) _i The weight of the ith multivariate Gaussian distribution component is satisfied with w ₁ +w ₂ +L+w _K ＝1；

3. The method for estimating the Bayesian state of the unobservable power distribution network based on the embedded power flow neural network according to claim 1, wherein the method comprises the following steps of: the specific steps of the step 2 include:

and (3) performing Monte Carlo sampling on the two-dimensional Gaussian mixture probability distribution of the active power and the reactive power injected into each node learned based on the limited data in the step (1), and performing random sampling from a known probability density function to realize mathematical simulation of the problem to be solved, so as to acquire sufficient node injection power data and obtain a large number of injection power samples.

4. The method for estimating the Bayesian state of the unobservable power distribution network based on the embedded power flow neural network according to claim 1, wherein the method comprises the following steps of: the specific method of the step 3 is as follows:

5. The method for estimating the Bayesian state of the unobservable power distribution network based on the embedded power flow neural network according to claim 1, wherein the method comprises the following steps of: the specific steps of the step 4 include:

(1) Structural design of neural network

The method comprises the steps of adopting a fully-connected neural network, and calculating an output result by forward propagation based on training data and weight parameters, wherein the fully-connected neural network consists of an input layer, an output layer and a plurality of hidden layers; the gradient of the loss function to each parameter is calculated through the derivative chain rule by back propagation, and the parameter is updated according to the gradient; the minimum loss function is used as a target, and the network parameters are optimized through forward and reverse repeated iteration;

(2) Establishing a loss function of the neural network:

is a state estimation value vector;

the physical loss function expression is:

wherein:

based on the state estimation result ∈>

The calculated node injection complex power vector, node injection active power vector, node injection reactive power vector, node complex voltage vector and node injection complex current vector; p, Q, U, I are true value vectors of node injection active power, node injection reactive power, node complex voltage and node injection complex current respectively; y is the node admittance matrix; * Is complex conjugate operation; e is the vector multiplication operation by element;

loss＝α·loss _physics +(1-α)·loss _MAE (4)

wherein: alpha is a super parameter for adjusting the weight of two loss, and alpha is more than or equal to 0 and less than or equal to 1;

6. The method for estimating the Bayesian state of the unobservable power distribution network based on the embedded power flow neural network according to claim 1, wherein the method comprises the following steps of: the specific method in the step 5 is as follows: