CN117350170A - Nonlinear oscillation analysis method based on KOOPHAN deep neural network - Google Patents

Nonlinear oscillation analysis method based on KOOPHAN deep neural network Download PDF

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CN117350170A
CN117350170A CN202311546040.1A CN202311546040A CN117350170A CN 117350170 A CN117350170 A CN 117350170A CN 202311546040 A CN202311546040 A CN 202311546040A CN 117350170 A CN117350170 A CN 117350170A
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neural network
koophan
deep neural
network model
koopman
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CN117350170B (en
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周一辰
李金泽
李永刚
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North China Electric Power University
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North China Electric Power University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/048—Activation functions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/0499—Feedforward networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/0985—Hyperparameter optimisation; Meta-learning; Learning-to-learn
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2123/00—Data types
    • G06F2123/02—Data types in the time domain, e.g. time-series data
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention disclosesA nonlinear oscillation analysis method based on a KOOPHAN deep neural network belongs to the technical field of nonlinear characteristic analysis of an electric power system, and comprises the following steps: simulation setting of power system fault scene and making of data set-construction of deep neural network model embedded with KOOPMAN operator-training of model-testing and adjusting of model-saving of model meeting set precision requirement-extracting KOOPMAN operator from saved deep neural network model embedded with KOOPMAN operatorCalculation ofAnd (3) the mode and the mode of the power system are adopted to realize the nonlinear oscillation characteristic analysis of the power system. The nonlinear oscillation analysis method based on the KOOPHAN deep neural network can simplify the nonlinear oscillation characteristic analysis process of the power system, maintain higher precision, realize high-precision prediction of time sequence tracks at any time step, accurately identify the system mode and describe the nonlinear oscillation characteristics of the power system.

Description

Nonlinear oscillation analysis method based on KOOPHAN deep neural network
Technical Field
The invention relates to the technical field of nonlinear characteristic analysis of an electric power system, in particular to a nonlinear oscillation analysis method based on a KOOPHAN deep neural network.
Background
With the rapid development of large-scale new energy power generation, high-voltage direct current transmission and high-power direct current load, the degree of power electronization of each part of a power system 'source-network-load' is improved year by year, so that the system presents strong nonlinear characteristics, and the nonlinear oscillation characteristics of the power system are more difficult to effectively analyze.
Because of extremely high difficulty in nonlinear oscillation characteristic analysis of a power system, the current accurate and practical analysis tools are still not more, and mainly comprise a normal shape method, a modal series method and a dimension-reducing Carleman embedding method. The normal form method and the modal series method are both required to be subjected to relatively complex high-dimensional nonlinear transformation, so that the operation is difficult and the time consumption is relatively long; the dimension reduction Carleman embedding method has the problem of "disastrous" model dimension caused by the increase of the order of a variable, and the higher-order modal analysis is seriously influenced when the calculated amount is increased.
Disclosure of Invention
In order to solve the problems, the invention provides a nonlinear oscillation analysis method based on a KOOPHAN deep neural network, which aims to simplify the nonlinear oscillation characteristic analysis process of an electric power system and simultaneously maintain higher precision so as to realize the aim of arbitrary time stepsAnd->The time sequence track of the system is predicted with high precision, the system mode is accurately identified, and the nonlinear oscillation characteristic of the power system is described.
In order to achieve the above object, the present invention provides a nonlinear oscillation analysis method based on a KOOPMAN deep neural network, comprising the steps of:
s1, simulating and setting a power system fault scene to obtain a generator rotor angleAnd electrical angular velocity>And creating a data set;
s2, dividing the data set into a training set and a testing set, and preprocessing the data;
s3, constructing a deep neural network model embedded with KOOPHAN operators;
s4, inputting the training set preprocessed in the step S2 into a built depth neural network model embedded with KOOPHAN operators, training the depth neural network model embedded with the KOOPHAN operators, and updating network parameters through forward calculation and backward propagation to minimize a loss function value;
s5, testing and adjusting a deep neural network model embedded with KOOPHAN operators;
s6, storing a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with the KOOPHAN operatorsAnd electrical angular velocity>Realize arbitrary->Generator rotor angle under time step->And electrical angular velocity>Is used for predicting the time sequence track of the (a);
s7, extracting the KOOPHAN operator from the deep neural network model with the embedded KOOPHAN operator stored in the step S6Calculate->And (3) the mode and the mode of the power system are adopted to realize the nonlinear oscillation characteristic analysis of the power system.
Preferably, the step S1 specifically includes the following steps:
s11, setting a scene of three-phase short circuit fault of the power system in a simulation manner, and determining a time stepCalculating limit cut time +.>Setting fault clearing time->Wherein->By changing->Obtaining the value of generator rotor angle after fault clearing>And electrical angular velocity>Is a time series data sample of (a);
s12, to be acquiredAnd->The data samples are made into a data set:
（1）
in the method, in the process of the invention,representing the->A sample number; />Representation and->Corresponding->A plurality of target samples; />Representing the total number of samples.
Wherein,and->All include->And->Specifically, the time sequence data of (a) is:
（2）
（3）
in the method, in the process of the invention,and->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->；/>And->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->。
Preferably, the step S2 specifically includes the following steps:
s21, dividing the data set into a training set and a testing set;
s22, calculating the mean value and variance of the training set sample, carrying out standardization processing on the training set sample, then taking the same mean value and variance, carrying out standardization processing on the testing set sample, wherein the calculation formula is as follows:
（4）
in the method, in the process of the invention,representing the mean of the data samples; />Representing the variance of the data samples; />And->Representing the data samples before and after the normalization process, respectively.
Preferably, the step S3 specifically includes the following steps:
s31, determining the basic structure, the network layer number and the neuron number of each layer of the deep neural network model to obtain the deep neural network model;
s32, determining the order of KOOPHAN operators to obtain KOOPHAN operators;
s33, embedding the KOOPHAN operator obtained in the step S32 into the deep neural network model obtained in the step S31 to obtain a deep neural network model embedded with the KOOPHAN operator;
s34, determining an activation function, an optimizer and a loss function of the deep neural network model embedded with the KOOPHAN operator.
Preferably, the deep neural network model in step S31 has 10 layers, wherein the first 5 layers form a network one, and the network one includes 1 input layer, 1 output layer and 3 hidden layers, the input layer is provided with 2 neurons, the output layer is provided with 64 neurons, and the 3 hidden layers are provided with 256 neurons; the latter 5 layers form a second network, the structure of the second network is the same as that of the first network, 64 neurons are arranged on an input layer of the second network, 2 neurons are arranged on an output layer of the second network, and 256 neurons are arranged on 3 hidden layers of the second network;
KOOPMAN operator described in step S32Is a square matrix, is provided with->Is of the order 64, will->Is embedded between the first and second networks for connecting the first and second networks, the operator ∈>The concrete structure is as follows:
（5）
in the method, in the process of the invention,representation->Is the order of (2); />Representation->Middle->Line->The element corresponding to the column;
the activation function in step S34 is a ReLU function, the optimizer is Adam, and the loss function is expressed as:
（6）
in the method, in the process of the invention,indicate->An input of a first time step network; />Indicate->An input of a first time step network; />Representing KOOPMAN operators; />And->Respectively representing a nonlinear function of the first fitting and the second fitting of the network; />、/>Andis the weight coefficient of the corresponding item.
Preferably, in step S4, the network output and parameter update formula of each layer is:
（7）
（8）
in the method, in the process of the invention,indicate->Layer output; />Indicate->Layer output; />Is->Layer and->Weights between layers, ++>For update +.>Layer and->Weights between layers, ++>For update +.>Layer and->Bias between layers; />Is->Layer and->Bias between layers; />Is an activation function; />Representing a learning rate; />And->Respectively correcting the deviation of the weight and the bias gradient accumulation in the loss function training process; />And->Deviation correction of the weights and bias gradient cumulative amount squares, respectively; />Is a smooth term.
Preferably, the step S5 specifically includes the following steps:
s51, inputting the test set preprocessed in the step S2 into a deep neural network model with embedded KOOPMAN operators trained in the step S4 to obtain a predicted generator rotor angleAnd electrical angular velocity>；
S52, judging whether the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement, if not, adjusting the super parameters of the depth neural network model embedded with the KOOPHAN operator, and returning to the step S4 for training until the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement.
Preferably, in step S52, the root mean square error and the average absolute error are used as precision evaluation indexes, and whether the deep neural network model embedded with the KOOPMAN operator meets the set precision requirement is determined;
the calculation formulas of the root mean square error RMSE and the average absolute error MAE are respectively as follows:
（9）
（10）
in the method, in the process of the invention,representing the true value +_>Representing the predicted value.
Preferably, the step S6 specifically includes the following steps:
preserving a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with KOOPHAN operatorsAnd electrical angular velocity>Predicting a next time step data generator rotor angle +.>And electrical angular velocity>Then->And->Reinjecting the deep neural network model embedded with KOOPMAN operator to obtain +.>And->Repeating the above operation until any +.>Step of time->And->Is described.
Preferably, in step S7, by calculationAnd screening dominant modes to realize nonlinear oscillation characteristic analysis of the power system.
The invention has the following beneficial effects:
(1) Can realize arbitrary time stepsAnd->The time sequence track prediction of the system is extremely high in prediction accuracy, complex mathematical modeling is not needed in the process, and only system simulation data are needed for data driving.
(2) By analyzing only the learned KOOPMAN operator using the strong learning ability of the deep neural networkThe system mode can be accurately identified, the nonlinear oscillation characteristic of the system can be described, and the method is simple and convenient to operate and accurate.
(3) The embedded KOOPMAN operator is utilized to enable the prediction process of the deep neural network model to have a complete theoretical basis, the interpretability and the reliability of the deep neural network model in the nonlinear time sequence evolution process of the power system are enhanced, the nonlinear dynamic characteristics of the system can be approximated in a stable domain range in a large range by virtue of the high-precision characteristic, and the application range of the small interference theory is expanded.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a logic diagram of a KOOPHAN deep neural network based nonlinear oscillation analysis method of the present invention;
FIG. 2 is a diagram of a neural network model structure of a nonlinear oscillation analysis method based on a KOOPHAN deep neural network of the present invention;
FIG. 3 is a diagram of a two-area four-machine test system of the nonlinear oscillation characteristic analysis method of the present embodiment;
fig. 4 is a rotor angle locus prediction diagram of the generator No. 1 versus the generator No. 4 of the present embodiment;
fig. 5 is a rotor angle locus prediction diagram of the generator No. 2 versus the generator No. 4 of the present embodiment;
FIG. 6 is a rotor angle trajectory prediction diagram of the generator No. 3 versus the generator No. 4 of the present embodiment;
FIG. 7 is a graph showing the nonlinear oscillation trace prediction comparison between the LSTM and the two-area four-machine test system according to the present invention;
fig. 8 is a graph showing the nonlinear oscillation trace prediction comparison between the present invention and the two-area four-machine test system by DMD and EDMD.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein. Examples of the embodiments are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements throughout or elements having like or similar functionality.
It should be noted that the terms "comprises" and "comprising," along with any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or server that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or apparatus, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
In the description of the present invention, it should be noted that, directions or positional relationships indicated by terms such as "upper", "lower", "inner", "outer", etc., are directions or positional relationships based on those shown in the drawings, or those that are conventionally put in use, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the apparatus or elements to be referred to must have a specific direction, be constructed and operated in a specific direction, and thus should not be construed as limiting the present invention.
In the description of the present invention, it should also be noted that, unless explicitly specified and limited otherwise, the terms "disposed," "mounted," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In recent years, with the rapid development of deep learning technology, a nonlinear relationship between input and output is established depending on strong learning ability, and an advantageous tool is provided for processing time series data. Meanwhile, the KOOPMAN operator theory is a nonlinear system mode analysis method, and can rely on the KOOPMAN operator to promote time sequence linear evolution in an infinite dimensional space without losing any information of the system. Based on this disclosure the following examples are disclosed:
as shown in fig. 1, the nonlinear oscillation analysis method based on the KOOPMAN deep neural network comprises the following steps:
s1, simulating and setting power system fault sceneAcquiring a rotor angle of a generatorAnd electrical angular velocity>And creating a data set;
preferably, the step S1 specifically includes the following steps:
s11, setting a scene of three-phase short circuit fault of the power system in a simulation manner, and determining a time stepCalculating limit cut time +.>Setting fault clearing time->Wherein->By changing->Obtaining the value of generator rotor angle after fault clearing>And electrical angular velocity>Is a time series data sample of (a);
s12, to be acquiredAnd->The data samples are made into a data set:
（1）
in the method, in the process of the invention,representing the->A sample number; />Representation and->Corresponding->A plurality of target samples; />Representing the total number of samples.
Wherein,and->All include->And->Specifically, the time sequence data of (a) is:
（2）
（3）
in the method, in the process of the invention,and->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->；And->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->。
S2, dividing the data set into a training set and a testing set, and preprocessing the data;
preferably, the step S2 specifically includes the following steps:
s21, dividing the data set into a training set and a testing set;
s22, calculating the mean value and variance of the training set sample, carrying out standardization processing on the training set sample, then taking the same mean value and variance, carrying out standardization processing on the testing set sample, wherein the calculation formula is as follows:
（4）
in the method, in the process of the invention,representing the mean of the data samples; />Representing the variance of the data samples; />And->Representing the data samples before and after the normalization process, respectively.
S3, constructing a deep neural network model embedded with KOOPHAN operators;
preferably, the step S3 specifically includes the following steps:
s31, determining the basic structure, the network layer number and the neuron number of each layer of the deep neural network model to obtain the deep neural network model;
preferably, as shown in fig. 2, the deep neural network model in step S31 has 10 layers, where the first 5 layers form a network one, and the network one includes 1 input layer, 1 output layer and 3 hidden layers, where the input layer is provided with 2 neurons, the output layer is provided with 64 neurons, and the 3 hidden layers are provided with 256 neurons; the latter 5 layers form a second network, the structure of the second network is the same as that of the first network, 64 neurons are arranged on an input layer of the second network, 2 neurons are arranged on an output layer of the second network, and 256 neurons are arranged on 3 hidden layers of the second network; at this time, the first network is not connected with the second network;
s32, determining the order of KOOPHAN operators to obtain KOOPHAN operators;
KOOPMAN operator described in step S32Is a square matrix, is provided with->Is of the order 64, will->Is embedded between the first and second networks for connecting the first and second networksTo promote the deep neural network model to better find nonlinear characteristics, the model is prevented from being excessively fitted to cause high-frequency fluctuation, < >>In the form of a learnable oblique symmetry matrix with positive diagonal elements, i.e. operator +.>The concrete structure is as follows:
（5）
in the method, in the process of the invention,representation->Is the order of (2); />Representation->Middle->Line->Column-corresponding element +.>；
S33, embedding the KOOPHAN operator obtained in the step S32 into the deep neural network model obtained in the step S31 to obtain a deep neural network model embedded with the KOOPHAN operator;
s34, determining an activation function, an optimizer and a loss function of the deep neural network model embedded with the KOOPHAN operator.
The activation function in step S34 is a ReLU function, the optimizer is Adam, and the loss function is expressed as:
（6）
in the method, in the process of the invention,indicate->An input of a first time step network; />Indicate->An input of a first time step network; />Representing KOOPMAN operators; />And->Respectively representing a nonlinear function of the first fitting and the second fitting of the network; />、/>Andis the weight coefficient of the corresponding item.
More specifically, the loss function is expressed as:
；
；
；
；
wherein,loss for state reconstruction for ensuring +.>Is the reversibility of (2); />For KOOPHAN evolution penalty, for guaranteeing the operator +.>Reflecting the nature of the oscillation mode, wherein the characteristic inherent to the object is reflected, here the operator +.>The characteristic inherent to the oscillation mode is represented, so that the oscillation mode is reflected; />For state prediction loss, for ensuring +.>The operator calculates the accuracy.
S4, inputting the training set preprocessed in the step S2 into a built depth neural network model embedded with KOOPHAN operators, training the depth neural network model embedded with the KOOPHAN operators, and updating network parameters through forward calculation and backward propagation to minimize a loss function value;
preferably, in step S4, the network output and parameter update formula of each layer is:
（7）
（8）
in the method, in the process of the invention,indicate->Layer output; />Indicate->Layer output; />Is->Layer and->Weights between layers, ++>For update +.>Layer and->Weights between layers, ++>For update +.>Layer and->Bias between layers; />Is->Layer and->Bias between layers; />Is an activation function; />Representing a learning rate; />And->Respectively correcting the deviation of the weight and the bias gradient accumulation in the loss function training process; />And->Deviation correction of the weights and bias gradient cumulative amount squares, respectively; />For smooth items, it is generally taken +.>。
S5, testing and adjusting a deep neural network model embedded with KOOPHAN operators;
preferably, the step S5 specifically includes the following steps:
s51, inputting the test set preprocessed in the step S2 into a deep neural network model with embedded KOOPMAN operators trained in the step S4 to obtain a predicted generator rotor angleAnd electrical angular velocity>；
S52, judging whether the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement, if not, adjusting the super parameters of the depth neural network model embedded with the KOOPHAN operator, and returning to the step S4 for training until the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement.
Preferably, in step S52, the root mean square error and the average absolute error are used as precision evaluation indexes, and whether the deep neural network model embedded with the KOOPMAN operator meets the set precision requirement is determined;
the calculation formulas of the root mean square error RMSE and the mean absolute error MAE are respectively (the smaller the RMSE and the MAE values are, the higher the model prediction accuracy is):
（9）
（10）
in the method, in the process of the invention,representing the true value +_>Representing the predicted value.
S6, storing a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with the KOOPHAN operatorsAnd electrical angular velocity>Realize arbitrary->Generator rotor angle under time step->And electrical angular velocity>Is used for predicting the time sequence track of the (a);
preferably, the step S6 specifically includes the following steps:
preserving a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with KOOPHAN operatorsAnd electrical angular velocity>Predicting a next time step data generator rotor angle +.>And electrical angular velocity>Then->And->Reinjecting the deep neural network model embedded with KOOPMAN operator to obtain +.>And->Repeating the above operation until any +.>Step of time->And->Is described.
S7, extracting the KOOPHAN operator from the deep neural network model with the embedded KOOPHAN operator stored in the step S6Calculate->And (3) the mode and the mode of the power system are adopted to realize the nonlinear oscillation characteristic analysis of the power system.
Preferably, in step S7, by calculationAnd screening dominant modes to realize nonlinear oscillation characteristic analysis of the power system.
Examples
The embodiment takes a two-area four-machine simulation example as an example for explanation, and verifies the effectiveness and accuracy of the nonlinear oscillation characteristic analysis method based on the embedded KOOPMAN operator deep neural network model.
Time domain simulation is performed on the two-area four-machine test system shown in fig. 3, and buses 3-101 are arranged close to buses 101 at the positionThree-phase short-circuit fault->Time fault removal, calculating limit removal time +.>. And sets the fault removal time +.>Simulation time->Step size->For 500 time steps, 2667 groups +.>And->Is a time series data sample of the (c).
2667 groups of generators G1, G2 and G3 are set by taking generator No. 4 as a reference pointThe data sample is made into a data set, the data set is divided into a training set and a testing set according to the proportion of 7:3, and the training set and the testing set are subjected to standardized processing successively.
Constructing a embedded KOOPMAN operator deep neural network model shown in FIG. 2, wherein the activation function is a ReLU function, the optimizer is an Adam function, and the loss function is set as follows:
；
training and testing the embedded KOOPMAN operator deep neural network model, and continuously adjusting the super parameters to obtain final precision evaluation indexes RMSE=0.0038 and MAE=0.0030 so as to meet the precision requirement.
Preserving an embedded KOOPMAN operator deep neural network model meeting the precision requirement, and inputting an initial value、/>And->The predicted 499-step time sequence track is shown in fig. 4-6, and the prediction results are shown as fig. 4, from which it can be seen that the prediction accuracy of the invention is evaluated by RMSE and MAE, rmse=0.0038 and mae=0.0030, the prediction accuracy is extremely high, the prediction error is small and basically consistent with the result obtained by time domain simulation solution, and the nonlinear evolution behavior of the system can be accurately approximated in a large range.
To further verify the advantages of the present inventionMore preferably, it is compared with a common time series prediction method such as long short-term memory (LSTM) and a traditional KOOPMAN operator-propelled time evolution method such as dynamic mode decomposition (dynamic mode decomposition, DMD) and extended dynamic mode decomposition (extendeddynamic mode decomposition, EDMD) toFor example, the comparison results are shown in fig. 7 and 8, and the accuracy evaluation indexes of the respective methods are shown in table 1:
table 1 evaluation index results
；
As can be seen from table 1, rmse=0.0038 and mae=0.0030 of the present invention are both minimum, and have the highest prediction accuracy, which proves that the embedding of KOOPMAN operators further improves the time-series evolution capability of the neural network, so that the prediction accuracy is improved.
Extraction of KOOPMAN operators from stored neural network modelsCalculate->The results are shown in table 2, and compared with the conventional small signal analysis results shown in table 3.
TABLE 2 KOOPHAN master mode
；
TABLE 3 Small Signal analysis results
；
As can be seen from tables 2 and 3, the mode in the KOOPHANNER master modeMode->Compared with the regional pattern (pattern +.>Mode->) And section pattern (pattern->) Correspondingly, the KOOPMAN operator learned by the method can accurately identify different modes of the system and reflect nonlinear dynamic information of the system.
For example, mode in KOOPHAN master modeCompared with the interval mode (mode) in the traditional small signal analysis result) Correspondingly, means ++>Real and imaginary results and->The real part and the imaginary part of the KOOPMAN are closer to each other, and then the corresponding frequency and damping ratio result obtained through eigenvalue solution is closer to each other, which indicates that the KOOPMAN operator learned by the method can accurately identify the dominant mode of the system.
It should also be noted that,、/>、/>KOOPHAN operators learned through a neural network are subjected to characteristic decomposition to obtain a large number of KOOPHAN modes (KOOPHAN leading modes, wherein KOOPHAN operators K obtained through the training of the neural network are subjected to characteristic decomposition to obtain a large number of oscillation modes, the oscillation modes are subjected to mode screening to obtain KOOPHAN leading oscillation modes), and the leading modes obtained after screening (leading modes are frequently accompanied with false oscillation modes in the system oscillation modes under the influence of fault time, fault type and measurement noise), wherein the leading oscillation modes of the system can be screened according to a relative energy threshold value by calculating the relative energy weight of each oscillation mode;
、/>、/>the system is characterized in that the system is a small signal analysis result obtained by small signal mode analysis, wherein the system is linearized at a working point to obtain a system state matrix, and an oscillation mode obtained by characteristic decomposition of the state matrix is a small signal mode.
Therefore, by adopting the KOOPHAN-based nonlinear oscillation analysis method, the expression capacity of the model to the system dynamic characteristics is enhanced by embedding the KOOPHAN operator into the deep neural network model, and the nonlinear time sequence track of the power system is predicted more accurately. And then the nonlinear oscillation characteristics of the power system are reflected by solving the learned KOOPHAN operator mode and mode. The process does not need to carry out complex mathematical modeling on the system, only needs system simulation data to carry out data driving, simplifies the nonlinear oscillation characteristic analysis process of the power system, and can keep higher precision.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.

Claims (10)

1. The nonlinear oscillation analysis method based on the KOOPHAN deep neural network is characterized by comprising the following steps of: the method comprises the following steps:
s1, simulating and setting a power system fault scene to obtain a generator rotor angleAnd electrical angular velocity>And creating a data set;
s2, dividing the data set into a training set and a testing set, and preprocessing the data;
s3, constructing a deep neural network model embedded with KOOPHAN operators;
s4, inputting the training set preprocessed in the step S2 into a built depth neural network model embedded with KOOPHAN operators, training the depth neural network model embedded with the KOOPHAN operators, and updating network parameters through forward calculation and backward propagation to minimize a loss function value;
s5, testing and adjusting a deep neural network model embedded with KOOPHAN operators;
s6, storing a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with the KOOPHAN operatorsAnd electrical angular velocity>Realize arbitrary->Generator rotor angle under time step->And electrical angular velocity>Is used for predicting the time sequence track of the (a);
s7, extracting the KOOPHAN operator from the deep neural network model with the embedded KOOPHAN operator stored in the step S6Calculate->And (3) the mode and the mode of the power system are adopted to realize the nonlinear oscillation characteristic analysis of the power system.
2. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: the step S1 specifically comprises the following steps:
s11, setting a scene of three-phase short circuit fault of the power system in a simulation manner, and determining a time stepCalculating limit cut timeSetting fault clearing time->Wherein->By changing->Obtain the value of the rotor angle of the generator after fault clearingAnd electrical angular velocity>Is a time series data sample of (a);
s12, to be acquiredAnd->The data samples are made into a data set:
（1）
in the method, in the process of the invention,representing the->A sample number; />Representation and->Corresponding->A plurality of target samples; />Representing the total number of samples;
wherein,and->All include->And->Specifically, the time sequence data of (a) is:
（2）
（3）
in the method, in the process of the invention,and->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->；/>And->Respectively represent +.>Under the individual samples->Corresponding to the individual time steps->And->。
3. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: the step S2 specifically comprises the following steps:
s21, dividing the data set into a training set and a testing set;
s22, calculating the mean value and variance of the training set sample, carrying out standardization processing on the training set sample, then taking the same mean value and variance, carrying out standardization processing on the testing set sample, wherein the calculation formula is as follows:
（4）
in the method, in the process of the invention,representing the mean of the data samples; />Representing the variance of the data samples; />And->Representing the data samples before and after the normalization process, respectively.
4. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: the step S3 specifically comprises the following steps:
s31, determining the basic structure, the network layer number and the neuron number of each layer of the deep neural network model to obtain the deep neural network model;
s32, determining the order of KOOPHAN operators to obtain KOOPHAN operators;
s33, embedding the KOOPHAN operator obtained in the step S32 into the deep neural network model obtained in the step S31 to obtain a deep neural network model embedded with the KOOPHAN operator;
s34, determining an activation function, an optimizer and a loss function of the deep neural network model embedded with the KOOPHAN operator.
5. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 4, characterized in that: the deep neural network model described in step S31 has 10 layers in total, wherein the first 5 layers form a network one, which includes 1 input layer, 1 output layer and 3 hidden layers, the input layer is provided with 2 neurons, the output layer is provided with 64 neurons, and the 3 hidden layers are all provided with 256 neurons; the latter 5 layers form a second network, the structure of the second network is the same as that of the first network, 64 neurons are arranged on an input layer of the second network, 2 neurons are arranged on an output layer of the second network, and 256 neurons are arranged on 3 hidden layers of the second network;
KOOPMAN operator described in step S32Is a square matrix, is provided with->Is of the order 64, will->Is embedded between the first and second networks for connecting the first and second networks, the operator ∈>The concrete structure is as follows:
（5）
in the method, in the process of the invention,representation->Is the order of (2); />Representation->Middle->Line->The element corresponding to the column;
the activation function in step S34 is a ReLU function, the optimizer is Adam, and the loss function is expressed as:
（6）
in the method, in the process of the invention,indicate->An input of a first time step network; />Indicate->An input of a first time step network;representing KOOPMAN operators; />And->Respectively representing a nonlinear function of the first fitting and the second fitting of the network; />、/>And->Is the weight coefficient of the corresponding item.
6. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 5, characterized in that: in step S4, the network output and parameter update formulas of each layer are:
（7）
（8）
in the method, in the process of the invention,indicate->Layer output; />Indicate->Layer output; />Is->Layer and->Weights between layers, ++>For update +.>Layer and->Weights between layers, ++>For update +.>Layer and->Bias between layers;is->Layer and->Bias between layers; />Is an activation function; />Representing a learning rate; />And->Respectively correcting the deviation of the weight and the bias gradient accumulation in the loss function training process; />And->Deviation correction of the weights and bias gradient cumulative amount squares, respectively; />Is a smooth term.
7. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: the step S5 specifically comprises the following steps:
s51, inputting the test set preprocessed in the step S2 into a deep neural network model with embedded KOOPMAN operators trained in the step S4 to obtain a predicted generator rotor angleAnd electrical angular velocity>；
S52, judging whether the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement, if not, adjusting the super parameters of the depth neural network model embedded with the KOOPHAN operator, and returning to the step S4 for training until the depth neural network model embedded with the KOOPHAN operator meets the set precision requirement.
8. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 7, characterized in that: in step S52, the root mean square error and the average absolute error are used as precision evaluation indexes, and whether the depth neural network model embedded with the KOOPMAN operator meets the set precision requirement is determined;
the calculation formulas of the root mean square error RMSE and the average absolute error MAE are respectively as follows:
（9）
（10）
in the method, in the process of the invention,representing the true value +_>Representing the predicted value.
9. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: the step S6 specifically comprises the following steps:
preserving a depth neural network model embedded with KOOPHAN operators meeting the set precision requirement, and inputting an initial generator rotor angle into the depth neural network model embedded with KOOPHAN operatorsAnd electrical angular velocity>Predicting a next time step data generator rotor angle +.>And electrical angular velocity>Then->And->Reinjecting the deep neural network model embedded with KOOPMAN operator to obtain +.>And->Repeating the above operation until any +.>Step of time->And->Is described.
10. The KOOPMAN deep neural network-based nonlinear oscillation analysis method according to claim 1, characterized in that: by calculation in step S7And screening dominant modes to realize nonlinear oscillation characteristic analysis of the power system.
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