CN110224401B - Power system transient stability prediction method combining artificial features and residual error network - Google Patents

Abstract

The invention relates to a power system transient stability prediction method combining artificial features and a residual error network, and belongs to the technical field of power system stability analysis. The method comprises the steps of collecting variables of the generator after fault removal to form an initial characteristic vector; extracting artificial features from the initial features according to artificial setting, arranging the initial feature vectors into three-dimensional data, automatically extracting the features by using a residual error unit in a depth residual error network, taking the automatically extracted features and the artificial features together as input of a full-connection layer, and obtaining transient stability prediction output after processing by two full-connection layers to form a structure of a transient stability prediction model; and finally, carrying out iterative solution by using the training sample set and the verification sample set to obtain relatively excellent model parameters, thereby obtaining a final transient stability prediction model and using the model for transient stability prediction. According to the method, the prediction accuracy of the transient stability of the power system can be improved through the combination of the artificial features and the residual error unit in the depth residual error network and the preferred selection of the model parameters.

Description

Power system transient stability prediction method combining artificial features and residual error network

Technical Field

The invention relates to a power system transient stability prediction method combining artificial features and a residual error network, and belongs to the technical field of power system stability analysis.

Background

The transient stability damage is an important reason for large-scale power failure accidents of the power system, and how to quickly and accurately judge the transient stability of the system is one of the main problems to be considered for safety control of the power system. In recent years, the construction of smart power grids is deepened continuously, and the operation data collected in a power system is enriched and improved day by day, so that the transient stability prediction method driven by data is widely concerned by scholars at home and abroad.

Currently, input features for transient stability prediction models include manually extracted features and intelligently and automatically extracted features. The power system is a highly complex nonlinear system, an artificial feature extraction method inevitably needs to make ideal assumptions and simplification, correlation of each variable on the macro is difficult to reflect, and certain limitations exist. Recently, deep learning is rapidly developed in the aspects of theory, algorithm, application and the like, and partial scholars have developed research on the application of the deep learning in the field of transient stability analysis of power systems. The Chinese patent publication No. CN107391852A proposes to construct a transient stability evaluation model based on a deep belief network, so that the evaluation calculation speed and the evaluation precision are improved. Chinese patent publication No. CN107846012A proposes a method for extracting features of feature variables layer by using a stacked automatic encoder, and then constructing a stable classification model by using a convolutional neural network. The Chinese patent with the application publication number of CN108832619A provides a transient stability evaluation model constructed based on a deep convolutional neural network, and automatic feature extraction based on deep learning can comprehensively analyze historical and current data to form high-order features, so that the data can be more accurately, objectively and effectively expressed, and the defects of artificial design are reduced. The method for manually extracting the features and the method for automatically extracting the features by deep learning are not contradictory and conflict, and the transient stability prediction model with higher accuracy can be constructed only by fully combining two analysis methods to extract the features and realizing advantage complementation.

Disclosure of Invention

The invention aims to provide a power system transient stability prediction method combining artificial features and a residual error network, aiming at the defects of the prior art, the method for manually extracting the features and the method for automatically extracting the features through deep learning are combined to construct a transient stability prediction model with higher accuracy, and the transient stability prediction model is used for transient stability prediction to improve the transient stability prediction precision.

The invention provides a power system transient stability prediction method combining artificial features and a residual error network, which comprises the following steps:

(1) for an electric power system with N generators, time domain simulation calculation is carried out on transient stability of s operation conditions under f faults according to historical operation conditions of the electric power system and experience of operators to obtain feature vectors X of s × f operation scenes^kAnd transient stability y^kWhere the superscript k denotes the kth operation scenario, k is 1,2, …, s × f, y^kWith (0,1) meaning that the power system can remain transient stable after the fault is cleared, y^kThe fault clearing time is set according to manual experience, and the active power P of the generator at n sampling points after the fault is cleared in the k operation scene_Gi ^kGenerator rotor angle_i ^kAngular velocity omega of generator rotor_i ^kVoltage amplitude V of generator bus_Gi ^kAnd the voltage phase angle theta of the generator bus_Gi ^kForm a feature vector X^k：

X^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]

The subscript i represents the ith generator in the power system, i is 1,2, …, N, t represents the tth sampling point, t is 1,2, …, N, N is the number of artificially set sampling points, and the sampling frequency is selected as the rated frequency of the power system;

(2) according to the feature vector X in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]The following artificial features defined for the 30 × n individuals were calculated:

artificial features

Wherein 0_-Indicating the last sample value before the occurrence of a fault

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₅ ^k(t)＝Y₃ ^k(t)-Y₄ ^k(t)

Artificial characteristic Y₆ ^k(t)＝Y₂ ^k(t)/Y₁ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₁ ^k(t)＝Y₉ ^k(t)-Y₁₀ ^k(t)

Artificial characteristic Y₁₂ ^k(t)＝Y₈ ^k(t)/Y₇ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₇ ^k(t)＝Y₁₅ ^k(t)-Y₁₆ ^k(t)

Artificial characteristic Y₁₈ ^k(t)＝Y₁₄ ^k(t)/Y₁₃ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₃ ^k(t)＝Y₂₁ ^k(t)-Y₂₂ ^k(t)

Artificial characteristic Y₂₄ ^k(t)＝Y₂₀ ^k(t)/Y₁₉ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₉ ^k(t)＝Y₂₇ ^k(t)-Y₂₈ ^k(t)

Artificial characteristic Y₃₀ ^k(t)＝Y₂₆ ^k(t)/Y₂₅ ^k(t)

The above 30 × n personal characteristics Y_p ^k(t) performing a maximum-minimum normalization, wherein the subscript p is 1, …,30, to obtain the normalized artificial features

The normalized formula is:

(3) feature vector X of each scene^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Performing maximum and minimum normalization, and arranging into three-dimensional data according to generator dimension, variable dimension and time dimension

Then setting a convolution layer, a pooling layer, a residual error unit and a full connection layer, and combining the 30 × n normalized artificial features in the step (2)

Obtaining a structure of the transient stability prediction model M, specifically comprising the following steps:

(3-1) obtaining the characteristic vector X under each operation scene obtained in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Carrying out maximum and minimum normalization, wherein the normalization formula is as follows:

then, the normalized data is processed

Arranging into three-dimensional data according to generator dimension, time dimension and variable dimension

The three-dimensional data

Has a dimension of N × N × 5;

(3-2) combining the artificial features in the step (2) and a residual error network in deep learning to design and obtain a structure of a transient stability prediction model M, wherein input data of the M is the normalized artificial features obtained in the step (2)

And the three-dimensional data obtained in the step (3-1)

The output of M is O_k ²When O is present_k ²When the value is (0,1), it indicates that the power system can maintain transient stability in the k-th operation scenario, and when the value is O_k ²When the value is (1,0), which means that the power system cannot maintain transient stability in the kth operation scenario, the model M is formed by stacking a plurality of units as follows:

(3-2-1) convolutional layer

Using c convolution kernels w_lAnd a bias matrix V⁰For the three-dimensional data of the kth operation scene in the step (3-1)

Performing convolution operation to obtain a feature vector O_kWhere l is 1, …, c, convolution kernel w_lAnd a bias matrix V⁰Is the parameter to be solved, w, of step (4)_l∈R^a×d，R^a×dRepresenting a × d-dimensional matrix, wherein each element in the matrix is a real number, the values of a and d are odd numbers, a is less than or equal to N, d is less than or equal to N, and the number c of convolution kernels is more than or equal to 5;

(3-2-2) pooling layer

For the feature vector O_kPerforming maximum pooling to obtain pooled feature A_k ⁰；

(3-2-3) stacked m residual units

Pooling feature A of step (3-2-3) with m residual units stacked in a depth residual network_k ⁰And performing feature extraction, wherein the output of the f residual error unit is as follows:

where the superscript f is 1, …, m, m being the total number of residual units, the value of m being set artificially, σ () being the ReLU activation function,

is the output of the f-th residual unit,

is the output of the f-1 th residual unit, J_l ^f,1Is the first convolution kernel of the first layer convolution layer used by the f-th order residual error unit, J_l ^f,2Is the first convolution kernel of the second convolution layer used by the f-th residual unit, where l is 1, …, c, V^f,1Is the bias matrix of the first layer convolutional layer used by the f-th order residual unit, V^f,2Is the bias matrix of the second convolutional layer used by the f-th residual unit, convolutional kernel J_l ^f,1And J_l ^f,2Bias matrix V_l ^f,1And V_l ^f,2All parameters to be solved in the step (4);

(3-2-4) pooling layer

Output A to mth stage residual unit_k ^mPerforming maximum pooling to obtain pooled features Q_k；

(3-2-5) batch normalization layer

Pooling feature Q of step (3-2-4) using batch normalization method_kNormalization processing is carried out to obtain normalized characteristics U_k；

(3-2-6) tiling layer

Utilizing a tiling function to normalize the characteristic U of the step (3-2-5)_kTiling into h × 1-dimensional feature vector V_kWherein the size of h is represented by the normalized characteristic U_kThe dimension of (2) is determined;

(3-2-7) first fully-connected layer

Normalizing the post-human characteristics of 30 × n obtained in the step (2)

H × 1 dimension feature vector V of step (3-2-6)_kAre combined to Z_k，Z_kIs a (h +30 × n) × 1-dimensional vector, and then Z is added_kInputting the output into the first full connection layer to obtain the output O of the first full connection layer_k ¹：

O_k ¹＝σ(GZ_k+b¹)

Where superscript 1 denotes the first tier fully-connected tier, the weight matrix G ∈ R^g×h，R^g×hRepresenting a g × h-dimensional matrix, each element of which is a real number, and a bias vector b of a first layer fully-connected layer¹∈R^g×1，R^g×1Representing a vector of dimension g × 1, each element in the vector being a real number, g representing the output dimension of the fully-connected layer, the output dimension of the fully-connected layer being set by human, considering that in this patent there are only two fully-connected layers, the input dimension of the first fully-connected layer is d₁+30 × n, the output dimension of the second fully-connected layer is 2 × 1 d to represent transient stability or transient instability, the output dimension of the first fully-connected layer is set to be G ∈ (2, h +30 × n), the weight matrix G and the offset vector b¹All parameters to be solved in the step (4);

(3-2-8) second fully-connected layer

The output O of the step (3-2-7)_k ¹Inputting the output into the second full connection layer to obtain the output O of the second full connection layer_k ²：

O_k ²＝Softmax(HO_k ¹+b²)

Where superscript 2 denotes the second tier fully-connected tier, the weight matrix H ∈ R^2×g，R^2×gRepresenting a 2 × g-dimensional matrix, each element of which is a real number, and a bias vector b of a fully-connected layer of the second layer²∈R^2×1，R^2×1Representing a 2 × 1-dimensional vector in which each element is a real number, Softmax () being a Softmax activation function, a weight matrix H, and an offset vector b²All parameters to be solved in the step (4);

(4) iteratively calculating parameters to be solved in M according to the s × f samples obtained in the step (1) and a gradient descent algorithm based on adaptive moment estimation, namely an Adam algorithm, to obtain a final transient stability prediction model, and specifically comprising the following steps:

(4-1) randomly extracting s × f samples obtained in the step (1)

Using the sample as training set, and remaining

The samples are used as verification sets, wherein

Represents rounding down to 0.8 × s × f;

(4-2) set S ═ { e ═ e_max,A_max,M_maxIn which A is_maxIs the highest prediction accuracy, e, of the transient stability prediction model obtained in the iterative process_maxIs to obtain the highest prediction accuracy A_maxNumber of iterations of time, M_maxIs the e th_maxThe transient stability prediction model obtained by the secondary iteration records the iteration times as r, and the maximum iteration time is r_maxThe minimum number of iterations is r_minWherein r is_maxAnd r_minIs set by human and satisfies r_max＞r_minMore than or equal to 10, and setting the initial value of the iteration number r to be 0, e_maxInitial value of 0, A_maxHas an initial value of 0, model M_maxSetting to be null;

(4-3) comparing the iteration number r with the maximum iteration number r_maxAnd (3) comparison:

(4-3-1) if r is not less than r_maxM in the set S_maxAs a final power system transient stability prediction model;

(4-3-2) if r is less than r_maxIf so, enabling r to be r +1, and then, turning to the step (4-4);

(4-4) calculating all parameters to be solved of the model M in the step (3) by using the training set and the Adam algorithm in the step (4-1), wherein the parameters include w_l、V⁰、J_l ^f,1、J_l ^f,2、V_l ^f,1、V_l ^f,2、G、H、b¹And b²Obtaining a transient stability prediction model M corresponding to the current parameter_r；

(4-5) Using M_rPredicting the transient stability of all samples in the verification set in the step (4-1) to obtain prediction accuracy rate, and recording the prediction accuracy rate as A_rA is_rValue of (A) and_maxand (3) comparison:

(4-5-1) if A_r>A_maxThen e is ordered_max＝r，A_max＝A_r，M_max＝M_rUpdating to obtain a new set S, and then turning to the step (4-3);

(4-5-2) if A_r≤A_maxThen e will be_maxValue of (a) and r-r_minAre compared if r-r is satisfied_min≤e_maxIf r is less than or equal to r, the step is switched to the step (4-3), and if r-r is not satisfied_min≤e_maxStopping iteration if r is less than or equal to r, and taking M in the set S_maxAs a final power system transient stability prediction model;

(5) obtaining active power, a rotor angle, a rotor angular velocity, a voltage amplitude and a voltage phase angle of the generator after fault removal, calculating and inputting the active power, the rotor angle, the rotor angular velocity, the voltage amplitude and the voltage phase angle into the power system transient stability prediction model obtained in the step (4) to obtain a transient stability prediction result, and specifically comprising the following steps:

(5-1) calculating or directly acquiring measurement data of the wide area measurement information system of the power system by utilizing off-line time domain simulation to obtain the active power P of the generator with n sampling points after the fault is cleared_Gi(t) rotor angle of generator_i(t) generator rotor angular velocity ω_i(t) voltage amplitude V of generator bus_Gi(t) and the phase angle θ of the voltage of the generator bus_Gi(t) constituting an initial input feature, wherein t is 1, …, n;

(5-2) calculating the initial input features of the step (5-1) to obtain 30 multiplied by n normalized artificial features defined in the step (2);

(5-3) normalizing the initial input features by using the maximum and minimum normalization in the step (3-1) and then arranging the normalized initial input features into three-dimensional data of Nxnx5;

and (5-4) inputting the 30 multiplied by N normalized artificial features obtained in the step (5-2) and the Nmultiplied by N by 5 three-dimensional data obtained in the step (5-3) into the power system transient stability prediction model obtained in the step (4) together to obtain a transient stability prediction result of the power system.

The method for predicting the transient stability of the power system by combining the artificial features and the residual error network has the characteristics and advantages that:

the method comprises the steps of collecting active power of a generator, a rotor angle of the generator, rotor angular speed, voltage amplitude of a generator bus and a voltage phase angle of the generator bus within a period of time after fault removal to form an initial input characteristic; extracting artificial features from the initial input features according to manual setting, arranging the initial feature vectors into three-dimensional data according to generator dimensions, variable dimensions and time dimensions, processing by utilizing a convolution layer, a pooling layer, a residual unit, a pooling layer, a batch normalization layer and a layering layer in a depth residual network to obtain automatic extracted features, merging the artificial extracted features and the automatic extracted features as input of a full-link layer, processing by two full-link layers to obtain transient stability prediction output, and forming a transient stability prediction model structure combining the artificial features and the residual network; using the training sample set and the verification set to carry out iterative solution to obtain relatively excellent model parameters, thereby obtaining a final transient stability prediction model; and finally, acquiring initial input characteristics and inputting the initial input characteristics into the transient stability prediction model to obtain a transient stability prediction result. The method improves the accuracy of transient stability prediction by combining artificial features with a depth residual error network and preferentially selecting model parameters.

Drawings

FIG. 1 is a block flow diagram of the method of the present invention.

FIG. 2 is a schematic diagram of a transient stability prediction model involved in the method of the present invention.

Fig. 3 is a schematic diagram of three-dimensional input data involved in the method of the present invention.

FIG. 4 is a flow chart of the method of the present invention for constructing a transient stability prediction model in step (4).

Detailed Description

The flow chart of the method for predicting the transient stability of the power system by combining the artificial features and the residual error network is shown in fig. 1, and the method comprises the following steps:

(1) for an electric power system with N generators, time domain simulation calculation is carried out on transient stability of s operation conditions under f faults according to historical operation conditions of the electric power system and experience of operators to obtain feature vectors X of s × f operation scenes^kAnd transient stability y^kWhere the superscript k denotes the kth operation scenario, k is 1,2, …, s × f, y^kWith (0,1) meaning that the power system can remain transient stable after the fault is cleared, y^kThe fault clearing time is set according to manual experience, and the active power P of the generator at n sampling points after the fault is cleared in the k operation scene_Gi ^kGenerator rotor angle_i ^kAngular velocity omega of generator rotor_i ^kVoltage amplitude V of generator bus_Gi ^kAnd the voltage phase angle theta of the generator bus_Gi ^kForm a feature vector X^k：

X^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]

The subscript i represents the ith generator in the power system, i is 1,2, …, N, t represents the tth sampling point, t is 1,2, …, N, N is the number of artificially set sampling points, the sampling frequency is selected as the rated frequency of the power system, the sampling frequency is 50Hz and N is 5 for the power system with the rated frequency of 50Hz, and the sampling frequency is 60Hz and N is 6 for the power system with the rated frequency of 60 Hz;

(2) according to the feature vector X in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]The following artificial features defined for the 30 × n individuals were calculated:

artificial features

Wherein 0_-Indicating the last sample value before the occurrence of a fault

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₅ ^k(t)＝Y₃ ^k(t)-Y₄ ^k(t)

Artificial characteristic Y₆ ^k(t)＝Y₂ ^k(t)/Y₁ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₁ ^k(t)＝Y₉ ^k(t)-Y₁₀ ^k(t)

Artificial characteristic Y₁₂ ^k(t)＝Y₈ ^k(t)/Y₇ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₇ ^k(t)＝Y₁₅ ^k(t)-Y₁₆ ^k(t)

Artificial characteristic Y₁₈ ^k(t)＝Y₁₄ ^k(t)/Y₁₃ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₃ ^k(t)＝Y₂₁ ^k(t)-Y₂₂ ^k(t)

Artificial characteristic Y₂₄ ^k(t)＝Y₂₀ ^k(t)/Y₁₉ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₉ ^k(t)＝Y₂₇ ^k(t)-Y₂₈ ^k(t)

Artificial characteristic Y₃₀ ^k(t)＝Y₂₆ ^k(t)/Y₂₅ ^k(t)

The above 30 × n personal characteristics Y_p ^k(t) performing a maximum-minimum normalization, wherein the subscript p is 1, …,30, to obtain the normalized artificial features

The normalized formula is:

(3) feature vector X of each scene^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Performing maximum and minimum normalization according to generator dimension and variable dimensionAnd time dimension arranged into three-dimensional data

Then setting a convolution layer, a pooling layer, a residual error unit and a full connection layer, and combining the 30 × n normalized artificial features in the step (2)

Obtaining the structure of the transient stability prediction model M, as shown in fig. 2, specifically includes the following steps:

(3-1) obtaining the characteristic vector X under each operation scene obtained in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Carrying out maximum and minimum normalization, wherein the normalization formula is as follows:

then, the normalized data is processed

Arranging into three-dimensional data according to generator dimension, time dimension and variable dimension

The three-dimensional data

Is N × N × 5, as shown in fig. 3;

(3-2) combining the artificial features in the step (2) and a residual error network in deep learning to design and obtain a structure of a transient stability prediction model M, wherein input data of the M is the normalized artificial features obtained in the step (2)

And the three-dimensional data obtained in the step (3-1)

The output of M is O_k ²When O is present_k ²When the value is (0,1), it indicates that the power system can maintain transient stability in the k-th operation scenario, and when the value is O_k ²When the value is (1,0), which means that the power system cannot maintain transient stability in the kth operation scenario, the model M is formed by stacking a plurality of units as follows:

(3-2-1) convolutional layer

Using c convolution kernels w_lAnd a bias matrix V⁰For the three-dimensional data of the kth operation scene in the step (3-1)

Performing convolution operation to obtain a feature vector O_kWhere l is 1, …, c, convolution kernel w_lAnd a bias matrix V⁰Is the parameter to be solved, w, of step (4)_l∈R^a×d，R^a×dRepresenting a × d-dimensional matrix, wherein each element in the matrix is a real number, the values of a and d are odd numbers, and satisfy a ≦ N, d ≦ N, the number c of convolution kernels is ≧ 5, and in one embodiment of the present invention, is selected as a ═ 3, d ═ 3, and c ═ 32;

(3-2-2) pooling layer

For the feature vector O_kPerforming maximum pooling to obtain pooled feature A_k ⁰In one embodiment of the invention, the step size of pooling is selected to be 2 × 2, of the pooling filterSize selected to be 2 × 2;

(3-2-3) stacked m residual units

Pooling feature A of step (3-2-3) with m residual units stacked in a depth residual network_k ⁰And performing feature extraction, wherein the output of the f residual error unit is as follows:

where the superscript f is 1, …, m, m being the total number of residual units, the value of m being set artificially, σ () being the ReLU activation function,

is the output of the f-th residual unit,

is the output of the f-1 th residual unit, J_l ^f,1Is the first convolution kernel of the first layer convolution layer used by the f-th order residual error unit, J_l ^f,2Is the first convolution kernel of the second convolution layer used by the f-th residual unit, where l is 1, …, c, V^f,1Is the bias matrix of the first layer convolutional layer used by the f-th order residual unit, V^f,2Is the bias matrix of the second convolutional layer used by the f-th residual unit, convolutional kernel J_l ^f,1And J_l ^f,2Bias matrix V_l ^f,1And V_l ^f,2All parameters to be solved in the step (4);

(3-2-4) pooling layer

Output A to mth stage residual unit_k ^mPerforming maximum pooling to obtain pooled features Q_kIn one embodiment of the invention, the step size of pooling is selected to be 2 × 2, the size of the pooling filter is selected to be 2 × 2;

(3-2-5) batch normalization layer

Pooling feature Q of step (3-2-4) using batch normalization method_kNormalization processing is carried out to obtain normalized characteristics U_k；

(3-2-6) tiling layer

Utilizing a tiling function to normalize the characteristic U of the step (3-2-5)_kTiling into h × 1-dimensional feature vector V_kWherein the size of h is represented by the normalized characteristic U_kThe dimension of (2) is determined;

(3-2-7) first fully-connected layer

Normalizing the 30 × n artificial features obtained in the step (2)

H × 1 dimension feature vector V of step (3-2-6)_kAre combined to Z_k，Z_kIs a (h +30 × n) × 1-dimensional vector, and then Z is added_kInputting the output into the first full connection layer to obtain the output O of the first full connection layer_k ¹：

O_k ¹＝σ(GZ_k+b¹)

Where superscript 1 denotes the first tier fully-connected tier, the weight matrix G ∈ R^g×h，R^g×hRepresenting a g × h-dimensional matrix, each element of which is a real number, and a bias vector b of a first layer fully-connected layer¹∈R^g×1，R^g×1Representing a vector of dimension g × 1, each element in the vector being a real number, g representing the output dimension of the fully-connected layer, the output dimension of the fully-connected layer being set by human, considering that in this patent there are only two fully-connected layers, the input dimension of the first fully-connected layer is d₁+30 × n, the output dimension of the second fully-connected layer is 2 × 1 d to represent transient stability or transient instability, the output dimension of the first fully-connected layer is set to be G ∈ (2, h +30 × n), the weight matrix G and the offset vector b¹All parameters to be solved in step (4) are parameters to be solved, and in one embodiment of the present invention, let g be 50;

(3-2-8) second fully-connected layer

The output O of the step (3-2-7)_k ¹Inputting the output into the second full connection layer to obtain the output O of the second full connection layer_k ²：

O_k ²＝Softmax(HO_k ¹+b²)

Where superscript 2 denotes the second tier fully-connected tier, the weight matrix H ∈ R^2×g，R^2×gRepresenting a 2 × g-dimensional matrix, each element of which is a real number, and a bias vector b of a fully-connected layer of the second layer²∈R^2×1，R^2×1Representing a 2 × 1-dimensional vector in which each element is a real number, Softmax () being a Softmax activation function, a weight matrix H, and an offset vector b²All parameters to be solved in the step (4);

(4) iteratively calculating parameters to be solved in the M according to the s × f samples obtained in the step (1) and a gradient descent algorithm based on adaptive moment estimation, namely an Adam algorithm, to obtain a final transient stability prediction model, wherein a flow chart of the model is shown in FIG. 4, and specifically comprises the following steps:

(4-1) randomly extracting s × f samples obtained in the step (1)

Using the sample as training set, and remaining

The samples are used as verification sets, wherein

Represents rounding down to 0.8 × s × f;

(4-2) set S ═ { e ═ e_max,A_max,M_maxIn which A is_maxIs the highest prediction accuracy, e, of the transient stability prediction model obtained in the iterative process_maxIs to obtain the highest prediction accuracy A_maxNumber of iterations of time, M_maxIs the e th_maxThe transient stability prediction model obtained by the secondary iteration records the iteration times as r, and the maximum iteration time is r_maxThe minimum number of iterations is r_minWherein r is_maxAnd r_minIs set by human and satisfies r_max＞r_minMore than or equal to 10, and setting the initial value of the iteration number r to be 0, e_maxInitial value of 0, A_maxHas an initial value of 0, model M_maxSet to null, in one embodiment of the inventionIn, r_maxIs set at 1000 times, r_minIs 50 times;

(4-3) comparing the iteration number r with the maximum iteration number r_maxAnd (3) comparison:

(4-3-1) if r is not less than r_maxM in the set S_maxAs a final power system transient stability prediction model;

(4-3-2) if r is less than r_maxIf so, enabling r to be r +1, and then, turning to the step (4-4);

(4-4) calculating all parameters to be solved of the model M in the step (3) by using the training set and the Adam algorithm in the step (4-1), wherein the parameters include w_l、V⁰、J_l ^f,1、J_l ^f,2、V_l ^f,1、V_l ^f,2、G、H、b¹And b²Obtaining a transient stability prediction model M corresponding to the current parameter_r；

(4-5) Using M_rPredicting the transient stability of all samples in the verification set in the step (4-1) to obtain prediction accuracy rate, and recording the prediction accuracy rate as A_rA is_rValue of (A) and_maxand (3) comparison:

(4-5-1) if A_r>A_maxThen e is ordered_max＝r，A_max＝A_r，M_max＝M_rUpdating to obtain a new set S, and then turning to the step (4-3);

(4-5-2) if A_r≤A_maxThen e will be_maxValue of (a) and r-r_minAre compared if r-r is satisfied_min≤e_maxIf r is less than or equal to r, the step is switched to the step (4-3), and if r-r is not satisfied_min≤e_maxStopping iteration if r is less than or equal to r, and taking M in the set S_maxAs a final power system transient stability prediction model;

(5) obtaining active power, a rotor angle, a rotor angular velocity, a voltage amplitude and a voltage phase angle of the generator after fault removal, calculating and inputting the active power, the rotor angle, the rotor angular velocity, the voltage amplitude and the voltage phase angle into the power system transient stability prediction model obtained in the step (4) to obtain a transient stability prediction result, and specifically comprising the following steps:

(5-1) calculation by means of off-line time domain simulation or directlyCollecting measurement data of a wide area measurement information system of the power system to obtain the active power P of the generator at n sampling points after the fault is cleared_Gi(t) rotor angle of generator_i(t) generator rotor angular velocity ω_i(t) voltage amplitude V of generator bus_Gi(t) and the phase angle θ of the voltage of the generator bus_Gi(t) constituting an initial input feature, wherein t is 1, …, n;

(5-2) calculating the initial input features of the step (5-1) to obtain 30 multiplied by n normalized artificial features defined in the step (2);

(5-3) normalizing the initial input features by using the maximum and minimum normalization in the step (3-1) and then arranging the normalized initial input features into three-dimensional data of Nxnx5;

and (5-4) inputting the 30 multiplied by N normalized artificial features obtained in the step (5-2) and the Nmultiplied by N by 5 three-dimensional data obtained in the step (5-3) into the power system transient stability prediction model obtained in the step (4) to obtain a transient stability prediction result of the power system.

Claims (1)

1. A power system transient stability prediction method combining artificial features and a residual error network is characterized by comprising the following steps:

(1) for an electric power system with N generators, time domain simulation calculation is carried out on transient stability of s operation conditions under f faults according to historical operation conditions of the electric power system and experience of operators to obtain feature vectors X of s × f operation scenes^kAnd transient stability y^kWhere the superscript k denotes the kth operation scenario, k is 1,2, …, s × f, y^kWith (0,1) meaning that the power system can remain transient stable after the fault is cleared, y^kThe fault clearing time is set according to manual experience, and the active power P of the generator at n sampling points after the fault is cleared in the k operation scene_Gi ^kGenerator rotor angle_i ^kAngular velocity omega of generator rotor_i ^kVoltage amplitude V of generator bus_Gi ^kAnd the voltage phase angle theta of the generator bus_Gi ^kForm a feature vector X^k：

X^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]

The subscript i represents the ith generator in the power system, i is 1,2, …, N, t represents the tth sampling point, t is 1,2, …, N, N is the number of artificially set sampling points, and the sampling frequency is selected as the rated frequency of the power system;

(2) according to the feature vector X in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]The following artificial features defined for the 30 × n individuals were calculated:

artificial features

Wherein 0_-Indicating the last sample value before the occurrence of a fault

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₅ ^k(t)＝Y₃ ^k(t)-Y₄ ^k(t)

Artificial characteristic Y₆ ^k(t)＝Y₂ ^k(t)/Y₁ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₁ ^k(t)＝Y₉ ^k(t)-Y₁₀ ^k(t)

Artificial characteristic Y₁₂ ^k(t)＝Y₈ ^k(t)/Y₇ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₁₇ ^k(t)＝Y₁₅ ^k(t)-Y₁₆ ^k(t)

Artificial characteristic Y₁₈ ^k(t)＝Y₁₄ ^k(t)/Y₁₃ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₃ ^k(t)＝Y₂₁ ^k(t)-Y₂₂ ^k(t)

Artificial characteristic Y₂₄ ^k(t)＝Y₂₀ ^k(t)/Y₁₉ ^k(t)

Artificial features

Artificial features

Artificial features

Artificial features

Artificial characteristic Y₂₉ ^k(t)＝Y₂₇ ^k(t)-Y₂₈ ^k(t)

Artificial characteristic Y₃₀ ^k(t)＝Y₂₆ ^k(t)/Y₂₅ ^k(t)

The above 30 × n personal characteristics Y_p ^k(t) performing a maximum-minimum normalization,where the subscript p is 1, …,30, resulting in normalized artificial features

The normalized formula is:

(3) feature vector X of each scene^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Performing maximum and minimum normalization, and arranging into three-dimensional data according to generator dimension, variable dimension and time dimension

Then setting a convolution layer, a pooling layer, a residual error unit and a full connection layer, and combining the 30 × n normalized artificial features in the step (2)

Obtaining a structure of the transient stability prediction model M, specifically comprising the following steps:

(3-1) obtaining the characteristic vector X under each operation scene obtained in the step (1)^k＝[P_Gi ^k(t),_i ^k(t),ω_i ^k(t),V_Gi ^k(t),θ_Gi ^k(t)]Carrying out maximum and minimum normalization, wherein the normalization formula is as follows:

then, the normalized data is processed

Arranging into three-dimensional data according to generator dimension, time dimension and variable dimension

The three-dimensional data

Has a dimension of N × N × 5;

(3-2) combining the artificial features in the step (2) and a residual error network in deep learning, designing and obtaining a structure of a transient stability prediction model M, wherein input data of the M is the normalized artificial features obtained in the step (2)

And the three-dimensional data obtained in the step (3-1)

The output of M is O_k ²When O is present_k ²When the value is (0,1), it indicates that the power system can maintain transient stability in the k-th operation scenario, and when the value is O_k ²When the value is (1,0), which means that the power system cannot maintain transient stability in the kth operation scenario, the model M is formed by stacking a plurality of units as follows:

(3-2-1) convolutional layer:

using c convolution kernels w_lAnd a bias matrix V⁰For the kth operation scenario in step (3-1)Three dimensional data

Performing convolution operation to obtain a feature vector O_kWhere l is 1, …, c, convolution kernel w_lAnd a bias matrix V⁰Is the parameter to be solved, w, of step (4)_l∈R^a×d，R^a×dRepresenting a × d-dimensional matrix, wherein each element in the matrix is a real number, the values of a and d are odd numbers, a is less than or equal to N, d is less than or equal to N, and the number c of convolution kernels is more than or equal to 5;

(3-2-2) pooling layer:

for the feature vector O_kPerforming maximum pooling to obtain pooled feature A_k ⁰；

(3-2-3) stacked m residual units:

pooling feature A of step (3-2-3) with m residual units stacked in a depth residual network_k ⁰And performing feature extraction, wherein the output of the f residual error unit is as follows:

A_k ^f＝σ(σ(A_k ^f-1*J_l ^f,1+V^f,1)*J_l ^f,2+V^f,2+A_k ^f-1)

where the superscript f is 1, …, m is the total number of residual units, m is set artificially, σ () is the ReLU activation function, a_k ^fIs the output of the f-th residual unit, A_k ^f-1Is the output of the f-1 th residual unit, J_l ^f,1Is the first convolution kernel of the first layer convolution layer used by the f-th order residual error unit, J_l ^f,2Is the first convolution kernel of the second convolution layer used by the f-th residual unit, where l is 1, …, c, V^f,1Is the bias matrix of the first layer convolutional layer used by the f-th order residual unit, V^f,2Is the bias matrix of the second convolutional layer used by the f-th residual unit, convolutional kernel J_l ^f,1And J_l ^f,2Bias matrix V_l ^f,1And V_l ^f,2Is the parameter to be solved in the step (4);

(3-2-4) a pooling layer:

output A to mth stage residual unit_k ^mPerforming maximum pooling to obtain pooled features Q_k；

(3-2-5) batch normalization layer:

pooling feature Q of step (3-2-4) using batch normalization method_kNormalization processing is carried out to obtain normalized characteristics U_k；

(3-2-6) leveling layer:

utilizing a tiling function to normalize the characteristic U of the step (3-2-5)_kTiling into h × 1-dimensional feature vector V_kWherein the size of h is represented by the normalized characteristic U_kThe dimension of (2) is determined;

(3-2-7) first full connection layer:

normalizing the 30 × n artificial features obtained in the step (2)

H × 1 dimension feature vector V of step (3-2-6)_kAre combined to Z_k，Z_kIs a (h +30 × n) × 1-dimensional vector, and then Z is added_kInputting the output into the first full connection layer to obtain the output O of the first full connection layer_k ¹：

O_k ¹＝σ(GZ_k+b¹)

Where superscript 1 denotes the first tier fully-connected tier, the weight matrix G ∈ R^g×h，R^g×hRepresenting a g × h-dimensional matrix, each element of which is a real number, and a bias vector b of a first layer fully-connected layer¹∈R^g×1，R^g×1Representing a vector of a dimension G × 1, wherein each element in the vector is a real number, G represents the output dimension of a full-connection layer, the output dimension of the full-connection layer of the first layer is set artificially, the value range is set as G ∈ (2, h +30 × n), a weight matrix G and an offset vector b¹Is the parameter to be solved in the step (4);

(3-2-8) second layer full connection layer:

the output O of the step (3-2-7)_k ¹Inputting the output into the second full connection layer to obtain the output O of the second full connection layer_k ²：

O_k ²＝Softmax(HO_k ¹+b²)

Where superscript 2 denotes the second tier fully-connected tier, the weight matrix H ∈ R^2×g，R^2×gRepresenting a 2 × g-dimensional matrix, each element of which is a real number, and a bias vector b of a fully-connected layer of the second layer²∈R^2×1，R^2×1Representing a 2 × 1-dimensional vector in which each element is a real number, Softmax () being a Softmax activation function, a weight matrix H, and an offset vector b²All parameters to be solved in the step (4);

(4) iteratively calculating parameters to be solved in M according to the s × f samples obtained in the step (1) and a gradient descent algorithm based on adaptive moment estimation, namely an Adam algorithm, to obtain a final transient stability prediction model, and specifically comprising the following steps:

(4-1) randomly extracting s × f samples obtained in the step (1)

Using the sample as training set, and remaining

The samples are used as verification sets, wherein

Represents rounding down to 0.8 × s × f;

(4-2) setting a set S ═ { e ═ e)_max,A_max,M_maxIn which A is_maxIs the highest prediction accuracy, e, of the transient stability prediction model obtained in the iterative process_maxIs to obtain the highest prediction accuracy A_maxNumber of iterations of time, M_maxIs the e th_maxThe transient stability prediction model obtained by the secondary iteration records the iteration times as r, and the maximum iteration time is r_maxThe minimum number of iterations is r_minWherein r is_maxAnd r_minIs set by human and satisfies r_max＞r_minMore than or equal to 10, the number of iterations is setThe initial value of the number r is 0, e_maxInitial value of 0, A_maxInitial value of-1, model M_maxSetting to be null;

(4-3) comparing the iteration number r with the maximum iteration number r_maxAnd (3) comparison:

(4-3-1) if r is not less than r_maxM in the set S_maxAs a final power system transient stability prediction model;

(4-3-2) if r is less than r_maxIf so, enabling r to be r +1, and then, turning to the step (4-4);

(4-4) calculating all parameters to be solved of the model M in the step (3) by using the training set and the Adam algorithm in the step (4-1), wherein the parameters include w_l、V⁰、J_l ^f,1、J_l ^f,2、V_l ^f,1、V_l ^f,2、G、H、b¹And b²Obtaining a transient stability prediction model M corresponding to the current parameter of the r-th iteration_r；

(4-5) Using M_rPredicting the transient stability of all samples in the verification set in the step (4-1) to obtain prediction accuracy rate, and recording the prediction accuracy rate as A_rA is_rValue of (A) and_maxand (3) comparison:

(4-5-1) if A_r>A_maxThen e is ordered_max＝r，A_max＝A_r，M_max＝M_rUpdating to obtain a new set S, and then turning to the step (4-3);

(4-5-2) if A_r≤A_maxThen e will be_maxValue of (a) and r-r_minAre compared if r-r is satisfied_min≤e_maxIf r is less than or equal to r, the step is switched to the step (4-3), and if r-r is not satisfied_min≤e_maxStopping iteration if r is less than or equal to r, and taking M in the set S_maxAs a final power system transient stability prediction model;

(5) obtaining active power, a rotor angle, a rotor angular velocity, a voltage amplitude and a voltage phase angle of the generator after fault removal, calculating and inputting the active power, the rotor angle, the rotor angular velocity, the voltage amplitude and the voltage phase angle into the power system transient stability prediction model obtained in the step (4) to obtain a transient stability prediction result, and specifically comprising the following steps:

(5-1) calculating or directly acquiring measurement data of the wide area measurement information system of the power system by utilizing off-line time domain simulation to obtain the active power P of the generator with n sampling points after the fault is cleared_Gi(t) rotor angle of generator_i(t) generator rotor angular velocity ω_i(t) voltage amplitude V of generator bus_Gi(t) and the phase angle θ of the voltage of the generator bus_Gi(t) constituting an initial input feature, wherein t is 1, …, n;

(5-2) calculating the initial input features of the step (5-1) to obtain 30 multiplied by n normalized artificial features defined in the step (2);

(5-3) normalizing the initial input features by using the maximum and minimum normalization in the step (3-1) and then arranging the normalized initial input features into three-dimensional data of Nxnx5;

and (5-4) inputting the 30 multiplied by N normalized artificial features obtained in the step (5-2) and the Nmultiplied by N by 5 three-dimensional data obtained in the step (5-3) into the power system transient stability prediction model obtained in the step (4) together to obtain a transient stability prediction result of the power system.

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