CN113435575A - Gate graph neural network transient stability evaluation method based on unbalanced data - Google Patents

Abstract

A gate graph neural network transient stability evaluation method based on unbalanced data belongs to the technical field of transient stability analysis of power systems. The present invention addresses the problem that current machine learning methods do not have interpretability. The present invention generates unstable samples based on Conditional Generative Adversarial Network (CGAN), which can not only generate unstable samples, but also can be used to generate unstable samples with unbalanced events, so that the samples can not only achieve a balance between stability and instability, but also Equilibrium of events in unstable samples is reached. After solving the data imbalance problem of the samples, the GGNN algorithm is used to evaluate the transient stability of the power system, and to determine the cause of the instability of the power system. Mainly used for transient stability assessment of power system.

Description

Transient stability evaluation method of gate graph neural network based on unbalanced data

technical field

The invention relates to a network transient stability evaluation method of a power system, and belongs to the technical field of transient stability analysis of a power system.

Background technique

Transient stability refers to whether the power system can reach the steady-state operating state or the original operating state through the transient process after a sudden large disturbance in a certain operating state. The power system is an important part of the energy Internet of Things, and the transient stability assessment of the power system is also very important. These large disturbances generally refer to short-circuit faults, sudden disconnection of lines or generators, etc. If the power system cannot reach a stable or original operating state after being subjected to large disturbances, it will cause the instability of the power system, cause the power system to collapse in a large area, and cause serious social and economic losses. Therefore, the designed TSA can quickly judge whether the system is unstable and analyze the instability events when the system is faulted, which is very necessary and of great significance.

The methods of transient stability analysis of power system include time-domain simulation method, direct method and machine learning method, among which the most mature method is time-domain simulation method. The time-domain simulation method is to establish a model for the whole system, that is, a high-dimensional nonlinear differential-algebraic equation. After solving the equation, the curve of each variable in the system with time is obtained, and then the transient stability of the system is judged. Because the model is established according to the physical characteristics of the components in the system and the network topology, the time domain simulation method is interpretable. The time-domain simulation method can be used as a test standard for other methods, but as the power system becomes more and more complex and the electronic hardware changes rapidly, the model of the time-domain simulation method becomes more and more complex, and the calculation becomes more and more complex. The time is getting longer and longer, which makes the time domain simulation method unable to judge the transient stability of the power system in real time. In addition, the time domain simulation method cannot obtain the stability margin of the transient stability of the power system.

The direct method is generally based on the energy function. There are three methods based on the energy function, namely the potential energy boundary surface method (PEBC), the controlled unstable equilibrium point method (CUEP) and the EEAC. Compared with the time domain simulation method, the direct method does not need to integrate the motion trajectory of the whole system step by step, which makes the calculation speed faster; and because the direct method first establishes the energy function, and then compares the energy of the system and the system at the time of fault removal. The energy at the critical time can judge the transient stability of the system, so the stability margin of the system can be obtained. However, the model adaptability of the direct method is poor, the judgment results are conservative and the energy when the system is in a critical state is difficult to obtain.

With the development of artificial intelligence, various methods of machine learning are also used for transient stability analysis of power systems, such as SVM, logistic regression, and deep learning. In the "DelayAware Intelligent Transient Stability Assessment System" by J.Q.Yu, A.Y.S.Lam, D.J.Hill and V.O.K.Li et al., the LSTM method not only solves the transient stability evaluation in the power system, but also solves the evaluation accuracy of the system model. and response time conversion and communication delay issues with PMUs. A cascaded CNN-based approach addresses the fast batch evaluation of the transient stability of power systems. With the development of graph learning, graph learning has also been applied to transient stability assessment of power systems. In Fast TransientStability Batch Assessment Using Cascaded Convolutional Neural Networks, a TSA model is built with a Recurrent Graph Convolutional Network (RGCN). Compared with other neural network methods, the TSA model based on graph attention neural network considers the influence of the topology of the power grid on the stability of the power system, and can achieve better accuracy to a certain extent. Compared with the time domain simulation method and the direct method, the machine learning method has the advantages of low computational complexity and the ability to obtain the stability margin, has a shorter response time, and can also realize real-time judgment of the transient stability of the power system. However, the current machine learning method is not interpretable, and the machine learning method is greatly affected by the imbalance of the data. The imbalance of the data will make the evaluation model have a high accuracy rate, but wrong judgment will occur. It causes a large loss, and at the same time, the generalization ability of the trained model is limited, so its robustness and applicability need to be improved.

SUMMARY OF THE INVENTION

The present invention addresses the problem that current machine learning methods do not have interpretability.

The transient stability evaluation method of gate graph neural network based on unbalanced data includes the following steps:

S1, collect the stability evaluation data of the power system, the stability evaluation data includes the bus voltage U1 and the operating parameters _of the motor, the operating parameters of the motor include the motor active power P, the motor reactive power Q, the motor voltage Amplitude U, motor current I;

S2. Use the transient stability assessment model to realize the stability assessment of the power system. The process of the transient stability assessment model to realize the stability assessment of the power system includes the following steps:

Generate a graph G(V,E) based on the stability evaluation data, where V represents the generator set and v∈V, select the generator set as the node v, and e _vw ∈ E is the edge between the nodes v and w; the motor active power P, the motor Reactive power Q, motor voltage amplitude U, motor current I are used to form the annotation vector of nodes, and bus voltage U ₁ is used to generate edges between nodes;

Based on the graph G(V,E), first use the first GGNN model to evaluate the transient stable instability state, if the output of the model is the transient stability of the power system, enter the next cycle; otherwise, use the second GGNN model to evaluate and continue Determine the type of events that cause system instability;

The first GGNN is a two-class model, and the output is a stable state and an unstable state; the second GGNN model is a multi-class model, and the output is an unstable type, corresponding to determine the cause of the instability of the power system;

The transient stability evaluation model is pre-trained, and the training process includes the following steps:

The stability evaluation data of the power system is collected as sample data. The operating parameters of the motor in the sample data also include the relative rotor angle δ of each generator. Based on the sample data of the relative rotor angle δ of each generator, the transient stability index is used to The steady state of the power system is divided into stable state and unstable state;

Then, for the data in the unstable state, the first CGAN is used to generate unstable samples, and the second CGAN is used to generate unstable samples of different events;

A graph G(V, E) is generated using samples from stable states and samples corresponding to unstable states, and trains a first GGNN model for evaluating transient stability and a second CGAN model for evaluating events corresponding to unstable samples.

Further, the first GGNN uses a gate recursive unit GRU in the propagation step.

Further, the second GGNN uses a gate recursive unit GRU in the propagation step.

其中l_i表示样本i的标签，h_i表示样本i的图级表示向量，i表示样本i，G表示样本量。Further, the loss function in the process of training the first GGNN model

where l _i represents the label of sample i, hi represents the graph-level representation vector of sample i, _i represents sample i, and G represents the sample size.

Further, the propagation recursive process of the first GGNN model is as follows:

表示为节点v在时间t的隐藏状态，x_v为节点v的节点注释向量；T表示向量的转置；in,

Represented as the hidden state of node v at time t, x _v is the node annotation vector of node v; T represents the transpose of the vector;

向量表示节点v在时间t收集的关于邻居节点的信息； A_v是图邻接矩阵的子矩阵，表示节点v及其邻居节点的连接状态；V表示节点的数量；

表示节点1在时刻t-1的隐藏状态，V表示节点的数量，

表示向量

的转置，b表示计算

的向量；Node v collects information from neighbor nodes;

A vector represents the information about neighbor nodes collected by node v at time t; A _v is a sub-matrix of the graph adjacency matrix, representing the connection state of node v and its neighbor nodes; V represents the number of nodes;

represents the hidden state of node 1 at time t-1, V represents the number of nodes,

representation vector

The transpose of , b represents the calculation

the vector;

表示节点v在时刻t的更新的信息，

表示节点v在时刻t的的信息，矩阵W^z和 W^r用来计算z和r的权重矩阵，矩阵U^z和U^r也用来计算z和r的权重矩阵；z和r表示更新门和重置门，σ表示sigmoid函数；in

represents the updated information of node v at time t,

Represents the information of node v at time t, the matrices W ^z and W ^r are used to calculate the weight matrix of z and r, and the matrices U ^z and U ^r are also used to calculate the weight matrix of z and r; z and r represent the update gate and Reset the gate, σ represents the sigmoid function;

where tanh(x) is the activation function, and ⊙ is the element-wise multiplication operation;

When graph-level output, the graph-level representation vector is defined as

充当软注意机制，该机制决定哪些节点与当前图级任务相关，i和 j是将

和x_v级联作为输入并输出实值的神经网络；h_g用于判断电力系统的暂态稳定性。in,

acts as a soft attention mechanism that decides which nodes are relevant to the current graph-level task, i and j are the

and x _v are cascaded as input and output real-valued neural network; h _g is used to judge the transient stability of the power system.

Further, h _g >0.5 of the first GGNN model indicates stability.

其中l₁表示为事件类型的标签，k表示事件类型的个数，a_j为激活函数softmax的输出。Further, the loss function in the process of training the second GGNN model

Among them, l ₁ represents the label of the event type, k represents the number of event types, and a _j is the output of the activation function softmax.

Further, before training the first GGNN model and the second CGAN model, the first CGAN and the second CGAN for generating unstable samples are pre-trained, and the training process includes the following steps:

The data data x of CGAN is constructed according to the stability evaluation data of the power system collected as the sample data:

x=[x ₁ ,x ₂ ,...,x _n ] (2)

a _i = [U ₁ PQUI δ] _1×89 (4)

Among them, n represents the number of input samples, and it can be known from equation (2)(3)(4) that the input data is n arrays of 500*89;

The input condition of the discriminator D of CGAN is the label vector of the sample data, which is an n×1 array;

Generate multi-label data based on sample data, each data has 2 labels:

L={l ₁ ,l ₂ } (5)

Among them, l ₁ represents the event that caused the data state, and l ₂ represents the stable state of the system;

l ₁ = {0, 1, 2, 3, 4} (6)

The event represented by l ₁ =0 is a short circuit event, the event represented by l ₁ =1 is a tap event, the event represented by l ₁ =2 is a load event, the event represented by l ₁ =3 is a switching event, and the event represented by l ₁ =4 The event is a synchronous generator event;

l ₂ = {0, 1} (7)

When l ₂ is 0, the sample is unstable; when l ₂ is 1, the sample is stable; L is an array with 1 row and 2 columns;

Based on the sample data and corresponding labels, the CGAN model corresponding to the generated unstable samples and the CGAN model corresponding to the unstable samples generated with different events are trained as the first CGAN model and the second CGAN model, respectively.

Further, in the process of collecting the stability evaluation data of the power system, the fault clearing time is recorded as time 0, and the bus voltage and motor operating parameters are collected according to the 0.01s time interval.

其中δ_max为仿真时长内任意两个发电机组最大的相对转子角。Further, the transient stability index

where _δmax is the maximum relative rotor angle of any two generator sets in the simulation duration.

Beneficial effects:

The invention generates unstable samples based on Conditional Generative Adversarial Network (CGAN), which can not only generate unstable samples, but also can be used to generate unstable samples with unbalanced events, so that the samples not only achieve a balance between stability and instability, but also can be used to generate unstable samples. Equilibrium of events in unstable samples is reached. After solving the data imbalance problem of the samples, the GGNN algorithm is used to evaluate the transient stability of the power system, and to determine the reasons for the instability of the power system. More importantly, the present invention considers the influence of different types of data, so the present invention can have a higher accuracy rate and a lower error rate. In addition, the CGAN of the present invention can not only solve the problem of data imbalance, but also take into account the category information when unstable, and cooperate with the subsequent GGNN to ensure that the present invention has better robustness and applicability to the evaluation model of the power system.

Through experiments, we can see that using CGAN can effectively and improve the performance of transient stability assessment to solve the data imbalance problem of power system transient stability assessment. GGNN can also quickly and accurately evaluate the transient stability of the power system, and can judge the reasons for the instability of the power system, and can also achieve good performance.

Description of drawings

Figure 1 shows the structure of the conditional generation network CGAN;

Fig. 2 is the curve of the relative rotor angle of each motor of the stable example of the IEEE-39 bus power system in England after suffering from a short-circuit event;

Fig. 3 is the curve of the relative rotor angle of each motor of the unstable sample of the IEEE-39 bus power system in England after suffering a short circuit event;

Figure 4 is a flow chart of CGAN generating unstable samples;

Figure 5 is the framework of the TSA model;

Fig. 6 is the graph structure corresponding to the structure of IEEE-39 bus system;

Fig. 7 is the structure of GRU;

Figure 8 is a flow chart of the model judging transient stability and predicting events that cause system instability;

Figure 9 shows the structure of the New England 39 bus system

Figure 10 is an iterative loss diagram of the generative model G;

Fig. 11 is the loss iteration diagram of discriminant model D;

Figure 12 shows the two-dimensional data space distribution of CGAN generated samples;

Figure 13 shows the accuracy of the proposed model under different proportions of destabilized samples;

Figure 14 is the result of the cause of unstable samples predicted by the GGNN model.

Detailed ways

Specific implementation one:

The method for evaluating the transient stability of a gate graph neural network based on unbalanced data described in this embodiment includes the following steps:

Step 1. First, use the first CGAN model to generate unstable samples, and then use the second CGAN model to generate unstable samples of different events:

1. Build a conditional generative adversarial network, namely CGAN:

Deep learning models can represent the probability distribution of various data in artificial intelligence applications. Adding discriminative models to deep learning can make the probability distribution of various data represented by the model more accurate. The generative adversarial network is a discriminative model added to deep learning. The generative adversarial network has both a generative model (G) and a discriminative model (D). The data distribution generated by the model conforms to the real data distribution.

Conditional Generative Adversarial Nets (Conditional Generative Adversarial Nets) is an extension of the original GAN. Both the generative model G and the discriminative model D add additional information y (condition). In the present invention, the condition is the category of the sample data, that is, label information.

Figure 1 shows the structure of the conditional generation network CGAN. As shown in Figure 1, the label y of the sample is used as part of the input layer of the discriminative model D and the generative model G. In the generative model G, the prior input noise z and sample labels y jointly form the joint hidden layer representation. In the discriminative model D, the input layer consists of real data x, label information y and data G(z|y) generated by the generative model. The condition y is added to the conditional generation network (CGAN) to generate the desired data. Due to the robustness of the power system, the unstable sample data is less. In order to solve the problem of data imbalance, the unstable sample is first obtained through CGAN. data.

The generative model G is used to obtain the real distribution of sample data, and generates similar real training data with noise z and condition y that obey a random distribution. The pursuit effect is that the closer the real data is, the better.

The discriminant model D is a binary classifier that judges the probability that a data comes from the real training data. If the data comes from the real training data, D outputs a large probability, otherwise, it outputs a small probability. Model G and D are trained at the same time: fix the discriminative model D, adjust the parameters of G to minimize the expectation of log(1-D(G(z|y))); fix the generative model G and adjust the parameters of D so that logD(x|y) )+log(1-D(G(z|y))) expectation maximization. This optimization process can be expressed as:

表示logD(x|y)的数学期望，

表示log(1-D(G(z|y)))的数学期望，V(D,G)为价值函数。in,

represents the mathematical expectation of logD(x|y),

Represents the mathematical expectation of log(1-D(G(z|y))), where V(D,G) is the value function.

2. Get data description:

Use phase measurement units (PMUs) to observe and transmit data in real time. When evaluating the transient stability of the power system online, the input data is the data measured by the PMUs 5 seconds after the fault is cleared, and then the transient stability of the power system is predicted based on the input data. In the present invention, time domain simulation is used to generate data, and FIG. 2 is a plot of the relative rotor angle of each motor for a stable example of an IEEE-39 bus power system in England after suffering a short circuit event. Figure 3 is a plot of the relative rotor angle of each machine for a sample of the instability of the IEEE-39 bus power system in England after suffering a short circuit event.

P,Q,U,I,δ为电机的运行参量，IEEE-39总线系统有10个电机，所以P＝(p₁,p₂,…,p₁₀)，Q＝(q₁,q₂,…,q₁₀)，U＝(u₁,u₂,…,u₁₀)， I＝(i₁,i₂,…,i₁₀)，δ＝(δ₁,δ₂,…,δ₁₀)。According to the Transient Stability Index (TSI), the stability criterion of the transient stability of the power system is the relative rotor angle or the generator rotor angle. . Because a large amount of data is needed to train the model so that the model can accurately judge the transient stability of the power system, the present invention selects the bus voltage U ₁ , the motor active power P, the motor reactive power Q, the motor voltage amplitude U, the motor The current I and the relative rotor angle δ of each generator are characteristic of the input data. The system selected by the present invention is the English IEEE-39 bus, so

P, Q, U, I, δ are the operating parameters of the motor. There are 10 motors in the IEEE-39 bus system, so P=(p ₁ ,p ₂ ,...,p ₁₀ ), Q=(q ₁ ,q ₂ , …,q ₁₀ ), U=(u ₁ ,u ₂ ,…,u ₁₀ ), I=(i ₁ ,i ₂ ,…,i ₁₀ ), δ=(δ ₁ ,δ ₂ ,…,δ ₁₀ ) .

The time when the system suffers a fault is -0.01s, the time 0 is the time when the fault is cleared, and the time interval is 0.01s. The input data of CGAN is shown below

x=[x ₁ ,x ₂ ,...,x _n ] (2)

a _i = [U ₁ PQUI δ] _1×89 (4)

Among them, n represents the number of input samples, and it can be known from equations (2) (3) (4) that the input data is n arrays of 500*89. The input condition of the discriminator D is the label vector of the sample data, which is an n×1 array.

3. Generation of multi-label data:

According to the results of the present invention, the research on the data of PMUs finds that the stable operation of the power system may lose its stability under the state of large disturbance, and the large disturbance is an emergency event that causes the system to become unstable. Therefore, in the present invention, each piece of data is set to have 2 tags:

L={l ₁ ,l ₂ } (5)

Among them, l ₁ represents the event that caused the data state, and l ₂ represents the steady state of the system.

l ₁ = {0, 1, 2, 3, 4} (6)

The event represented by l ₁ =0 is a short circuit event, the event represented by l ₁ =1 is a tap event, the event represented by l ₁ =2 is a load event, the event represented by l ₁ =3 is a switching event, and the event represented by l ₁ =4 The event is a synchronous generator event.

l ₂ = {0, 1} (7)

When _l2 is 0, the sample is unstable, and when _l2 is 1, the sample is stable. It can be known from the above formulas (5) (6) (7) that L is an array with 1 row and 2 columns.

4. Train the CGAN model corresponding to the unstable samples and the CGAN model corresponding to the unstable samples that generate different events, which are respectively recorded as the first CGAN model and the second CGAN model;

After studying the data, it is found that the accuracy of the power system transient stability assessment model is related to whether the instability samples and stable samples in the data are balanced. The balance of each event in CGAN is related to the balance of each event, so when the invention uses CGAN to generate unstable samples, not only the stable state of the sample, but also the event type of the sample is considered.

Therefore, when balancing the samples, the present invention firstly trains the CGAN for generating unstable samples based on _l2 , which is denoted as the first CGAN model; and then trains the CGAN for generating different types of unstable samples based on _l1 , which is denoted as the first CGAN model. Two CGAN models. Figure 4 shows the flow chart of CGAN generating unstable samples.

When generating unstable samples, the condition y=l ₂ , the optimization process of the value function is

where l ₂ ∈(0,1);

Considering the balance of each event in the unstable sample, the condition is y=l ₁ , and the optimization process of the value function is

where l ₁ ∈ (0,1,2,3,4).

In the process of actually generating unstable samples, firstly, unstable samples are generated through the first CGAN, and then unstable samples of different events are generated through the second CGAN.

Step 2: Use the transient stability evaluation model to evaluate the instability. In the process of the instability evaluation, a graph neural network is first generated based on the bus voltage and the operating parameters of the motor, and then the first GGNN model is used to evaluate the instability of the transient stability. state, and when it is unstable, the second GGNN model is used to evaluate the type of unstable state:

1. Construct a transient stability assessment model:

The transient stability evaluation model is a TSA model based on two GGNN models; the transient stability evaluation of the power system is to determine whether the system can return to a stable operating state within 0-10 seconds after the fault is removed. Prior to this, there have been many methods based on machine learning and data mining to achieve transient stability assessment of power systems. The key that the research can be applied to the real power system is to accurately judge the transient stability of the power system in the shortest time possible. In the present invention, when evaluating the transient stability of the system, the data of 5 seconds after the fault is cleared is selected to be used. The framework of the TSA model adopts the way of training the model offline and applying the model online. Online TSA has two modes, regular updates and real-time updates. Regular Updates: After training, the trained TSA model can be rapidly deployed when live data arrives, and the model is updated periodically with the number of newly collected samples. Real-time update: Offline training from a large amount of sample data, but can update itself online because the model performs transient stability assessment for the power system online. The latter can update the model quickly, but it is not general.

In the present invention, when the model is applied online, the method of regularly updating the model is selected. The framework of the proposed TSA model is shown in Figure 5. The CGAN model and the GGNN model are trained offline. When applied online, the trained GGNN transient stability evaluation model is directly used, and the newly evaluated PMU data is used to regularly update the training. Good TSA model.

(1) Build a graph neural network:

Graph neural network is proposed based on neural network, which is used to process and analyze graph-structured data. The present invention selects the IEEE-39 bus system to test whether the proposed TSA model is valid, and the IEEE-39 bus system is also a system often selected for testing the power system transient stability evaluation algorithm. The structure and diagram structure of the IEEE-39 bus system are shown in Figure 6. The system has 39 buses, 10 groups of units, 19 loads and 34 transmission lines.

其中

包含每个节点v邻节点的信息。h_v是节点v，s维的向量，能够用来生产输出 o_v，本发明中，o_v为节点的节点分数。图G(V,E)有一个图级别的标签，即样本图数据的标签l_G，l_G＝l₂＝{0,1}，标签为0即代表该电力系统失稳，标签为1即代表电力系统稳定。选择如下节点特征来描述节点，称为节点注释x_v，并使用向量x来表示这些注释。节点v的注释向量为Take the IEEE-39 bus system structure diagram G(V, E): V represents the generator set and v∈V, then v is a value from 1 to 10. Gensets are selected as nodes v, each node v is defined by its characteristics and associated nodes. e _vw ∈ E is the edge between nodes v and w, and the edge represents the relationship between nodes. The generator sets are connected by buses and transmission lines, and the relationship between nodes can be represented by the number of buses and transmission lines. If the number of buses and the length of the transmission line are large, the correlation between nodes is small, and edges between nodes are generated based on the bus voltage U1. Because the units and units, units and loads are connected to each other by transmission lines, so the graph G(V, E) is an undirected graph. The goal of a graph neural network (GNN) is to learn hidden states

in

Contains information about the neighbors of each node v. h _v is a node v, s-dimensional vector, which can be used to produce the output _ov . In the present invention, _ov is the node score of the node. Graph G(V,E) has a graph-level label, that is, the label of the sample graph data l _G , l _G =l ₂ ={0,1}, the label is 0, which means the power system is unstable, and the label is 1, which means that the power system is unstable. Represents the stability of the power system. The following node features are chosen to describe the nodes, called node annotations x _v , and a vector x is used to represent these annotations. The annotation vector for node v is

x _v =[p _v ,q _v ,u _v ,i _v ] ^T (10)

Among them, p, q, u, and i represent the active power, reactive power, voltage, and current of node v, respectively.

(2) Build the first GGNN model:

In the transient stability assessment of the power system, the nodes are fixed, static graph structures, characterized by time series data, and dynamic input information, and the stability assessment of the present invention is a classification problem. In the present invention, GGNN is used to judge the transient stability evaluation of the power system.

GGNN (Gated Graph Neural Network), uses a gate recursive unit GRU in the propagation step, expands the recursion for the number of steps T, and uses backpropagation to calculate the gradient. Figure 7 shows the structure of the GRU.

The basic recursion of the propagation model in the transient stability evaluation model of the power system is equations (11)-(16):

表示为节点v在时间t的隐藏状态，x_v为节点v的节点注释向量，T表示向量的转置。in,

is denoted as the hidden state of node v at time t, x _v is the node annotation vector of node v, and T is the transpose of the vector.

向量表示节点v在时间t收集的关于邻居节点的信息。 A_v是图邻接矩阵的子矩阵，表示节点v及其邻居节点的连接状态。V表示节点的数量，

表示节点1在时刻t-1的隐藏状态，V表示节点的数量，

表示向量

的转置，b表示计算

的向量。Node v gathers information from neighbor nodes.

A vector representing the information node v has collected about its neighbors at time t. A _v is a sub-matrix of the graph adjacency matrix, representing the connection state of node v and its neighbors. V represents the number of nodes,

represents the hidden state of node 1 at time t-1, V represents the number of nodes,

representation vector

The transpose of , b represents the calculation

vector.

表示节点v在时刻t的更新的信息，

表示节点v在时刻t的的信息，矩阵W^z和W^r用来计算z和r的权重矩阵，矩阵U^z和U^r也用来计算z和r的权重矩阵。z和r表示更新门和重置门，σ表示sigmoid函数，可表示为σ＝1/(1+exp(-x))。in

represents the updated information of node v at time t,

Represents the information of node v at time t, the matrices W ^z and W ^r are used to calculate the weight matrix of z and r, and the matrices U ^z and U ^r are also used to calculate the weight matrix of z and r. z and r represent the update gate and reset gate, and σ represents the sigmoid function, which can be expressed as σ=1/(1+exp(-x)).

where tanh(x) is the activation function and ⊙ is the element-wise multiplication. The propagation step of GGNN neural network is similar to GRU, which has an update function and is able to incorporate information from other nodes and the previous time step to update the hidden state of each node. When graph-level output, the graph-level representation vector is defined as

充当软注意机制，该机制决定哪些节点与当前图级任务相关，i和 j是将

和x_v级联作为输入并输出实值的神经网络。h_g能够判断电力系统的暂态稳定性。in,

acts as a soft attention mechanism that decides which nodes are relevant to the current graph-level task, i and j are the

A neural network that is cascaded with x _v as input and outputs real values. h _g can judge the transient stability of the power system.

So when training the model, when reducing the loss function, update the parameters of the model. The loss function is

where l _i represents the label of sample i, hi represents the graph-level representation vector of sample i, _i represents sample i, and G represents the sample size.

(3) Build a second GGNN model, use the first GGNN model to evaluate the transient stable instability state, and use the second GGNN model to evaluate the type of unstable state when it is unstable:

The transient stability assessment models of power systems based on other machine learning methods can only judge the transient stability of the system, while the transient stability assessment model based on GGNN proposed in the present invention can not only judge the transient stability, but also It can also be explanatory. In the training process, train an unstable GGNN that evaluates transient stability, denoted as the first GGNN model; train a GGNN that evaluates the unstable state, denoted as the second GGNN model; the output of the second GGNN model is unstable type, corresponding to the cause of the instability of the power system;

The propagation of the second GGNN model for judging the event type is the same as that of the first GGNN, the difference is that the second GGNN model for judging the event type is a multi-classification model. So the activation function and loss function of the output layer are also different from the first GGNN model. The activation function for event classification is softmax, and the loss function is categorical cross-entropy. The softmax function is expressed as

where j represents the jth neuron, and n is the number of neurons in the previous layer of the output layer.

where l ₁ represents the label of the event type, k represents the number of event types, and formula (20) is the loss function.

In the actual evaluation process, first use the first GGNN model to evaluate the unstable state of transient stability, if the output of the model is the transient stability of the power system (ie h _g > 0.5), enter the next cycle; otherwise, use the first The second GGNN model evaluation continues to determine the type of events that cause the system to destabilize. From this output, we can know the maximum possible type of events that cause transient instability of the system. Figure 8 shows the flow chart of the model for judging transient stability and predicting events that cause system instability.

Example

A. IEEE-39 bus system:

Verification of the validity of the TSA model with the New England 39 bus system. The simulation was performed on a PC with an Intel Core i3 CPU and 8.00GB RAM. The structure of the New England 39 bus system is shown in Figure 9. As shown in Figure 9, the system has 10 generators, 39 buses, 19 loads, 12 transformers and 34 transmission lines.

B. Data Generation

The dataset used for the experiments was constructed by performing time-domain simulation of the IEEE-39 bus system using powerfactory. By setting the fault type and the pre-defined stable state of the power system in advance, the numerical value of each attribute of each node of the power system under these two preset preconditions can be obtained when the time-domain simulation is started. The load of the stability analysis of this software is voltage-dependent, so the initial operating condition voltage amplitude is set to 1kpu-2kpu, the frequency is 60 Hz, and the standard voltage is 345kV. Before starting the simulation, the power flow calculation must be carried out, and the time domain simulation calculation can only be started when the power flow calculation results are converged.

Events considered by the present invention are short circuit events, synchronous generator events, load events, switching events and tap events. The short-circuit event is a three-phase ground short-circuit event, the location of the fault is a random location of all buses and connecting lines, the fault duration is 0.1s, and the duration of the time domain simulation is 5s. Finally, 1000 samples were obtained, including 580 stable samples and 420 unstable samples. The fault duration of the synchronous generator event, the switching event and the tap event are all 0.1s, and the duration of the time domain simulation is also 5s. The final sample numbers are 1000, 1000, and 102, respectively. Among them, there are 640 stable samples for synchronous generator events, 360 unstable samples, 570 stable samples for switching events, 430 unstable samples, and 60 stable samples for switching events. The number of unstable samples was 42. Load events have load changes ranging from 75% to 125% in 5% increments, failures have a duration of 0.1s and a duration of 5s, and last to 1000 samples, of which 650 are stable and 650 are unstable The sample is 350 pieces. Therefore, a total of 4102 samples were obtained through time domain simulation, of which 2500 were stable samples and 1502 were unstable samples. The obtained sample dimension is 10+10+10+10+10+39=89. Because the power system in real life is very stable, only in a few cases, the power system will be unstable, so in the actual data, there will be very few samples of instability. So, in order to simulate the situation of the real power system, some unstable samples are randomly discarded, so that the unstable samples account for 9% of the total samples.

Another definition of the transient stability of the power system is that after the power system in steady-state operation is subjected to large disturbances (various short-circuit faults, removal of large-capacity generators, substantial increase in load, etc.) The ability to run synchronously. The rotor angle δ is used as the criterion for judging the stability of the power system. Therefore, the transient stability index (TSI) of the relative rotor angle after disturbance is used to judge the stability of the sample, and its expression is:

In the formula, _δmax is the maximum relative rotor angle of any two generator sets in the simulation duration. If TSI>0, the system maintains a stable operating state; otherwise, the system is unstable.

In order to effectively evaluate the performance of the model, four test training sets are selected to test the training model. The dataset was randomly divided into training set and test set with ratios of 4:1, 3:1, 7:3 and 3:2. The experimental results on the training and test sets of various ratios are presented in the following sections.

C. Synthetic Data Visualization Analysis

Experiments show that the method proposed in the present invention can effectively solve the problem of high misjudgment rate caused by the data imbalance problem in the transient stability evaluation of the power system, and can achieve high accuracy.

In order to achieve sample balance, label samples are generated, and the labels (l ₁ and l ₂ ) of the samples are set as the condition y, and the input condition y of the discriminator D is the label. By changing the overall label of the sample to the event label of the sample, the unstable data of the event balance can be obtained. Then, it can not only solve the problem of stability imbalance of samples, but also solve the imbalance problem of events in unstable samples. Figures 10 and 11 respectively represent the loss iteration graphs of the generative model G and the discriminant model D. It can be seen from the figures that both the generative model G and the discriminant model D can achieve convergence, and the convergence speed is very fast.

Figure 12 presents the results of the data balancing of the proposed method, transforming the balanced data into a two-dimensional spatial distribution. In Figure 12, green points represent unstable samples in the original sample, red points represent stable samples in the original sample, and blue points represent unstable sample data generated by CGAN. It can be seen from the figure that the original number of unstable samples is small, and the generated unstable samples can reach a state of equilibrium with the stable samples, and the generated unstable samples do not overlap with the original samples, so the model can A relatively clear judgment of the type of the sample will not affect the accuracy of the sample.

These results can only show that CGAN can generate data that conforms to the original data distribution and can solve the problem of data imbalance. It is necessary to demonstrate that the generated new balanced dataset can indeed improve the performance of the transient stability evaluation model. Figure 13 shows the accuracy of the transient stability evaluation model of the power system under various sample ratios. As shown in Figure 13, when the proportion of data stable and unstable samples is large, the accuracy of the model is low. As the proportion of samples decreases, the accuracy of the model increases gradually. When the samples are balanced, the accuracy of the model increases. reach the highest.

In the present invention, a convolutional neural network (CNN) is selected as a comparative experiment. Compared with the results of the transient stability evaluation model of GGNN proposed by the present invention, the accuracy and precision of the method proposed by the present invention are higher. . To demonstrate the performance of the TSA models of these two methods, four metrics are selected, namely accuracy, precision, recall and F1 score. Table 1 and Table 2 show the results of the transient stability evaluation model performance of the two methods under different sample proportions. It can be seen from Table 1 that the minimum model accuracy is 30%, and its proportion is the proportion of unbalanced samples in the actual situation preset by the present invention, and the maximum model accuracy is 92.09%, which is the balanced sample data. accuracy of the model. Table 2 shows the results of the transient stability evaluation of the comparative experimental CNN training the model with different sample ratios. The unstable sample data generated by the CGAN proposed in the present invention can solve the problem of data imbalance without losing the performance of the model, whether it is the model proposed in the present invention or other models. It can be seen from the comparison between Table 1 and Table 2 that the GGNN transient stability evaluation model proposed by the present invention has higher accuracy than the CNN transient stability evaluation model.

Table 1. GGNN transient stability evaluation results with different proportions of samples

Table 2. CNN transient stability evaluation results with different proportions of samples

In order to prevent overfitting of the model and effectively improve the performance of the model, the present invention selects four different ratios of training and testing sets. As shown in Table 4, the results of the proposed transient stability evaluation model for four different training and testing sets of A, B, C, D are presented. Table 3 represents four different train-test set ratios. In Table 4, under the same training and test set, under balanced data, the results of the GGNN transient stability evaluation model, the performance indicators of each model are larger than the performance indicators of unbalanced data. It can be seen that CGAN can solve the problem of data imbalance.

Table 3. Proportions of different train-test sets

Table 4. GGNN transient stability evaluation results for different test training sets

As can be seen from the above figures and tables, it is feasible to use the CGAN algorithm to generate unstable samples to solve the problem of data imbalance in the transient stability assessment of the power system proposed by the present invention, and it will not lose the versatility and versatility of the data. performance of the model. The solution of the data imbalance problem is effective for improving the transient stability evaluation model of the power system. Compared with the imbalanced samples, the performance index of the model is relatively high when the samples are balanced.

D. GGNN model classification performance analysis

To show the effectiveness of the GGNN model used, a deep convolutional neural network CNN is used as a comparison algorithm. All results are obtained by training on the same training and test sets. The following table 5 shows the results of different training and test set proportions and different models in the transient stability evaluation of the power system. It can be seen from Table 5 that under the same training and test set ratio, the performance of the GGNN power system transient stability evaluation model is always better than that of the CNN model.

Table 5. Transient stability evaluation results for different train-test set proportions and models.

E. Judging cause performance analysis

Graph neural networks are explanatory, and GGNN is a type of graph learning, which is also explanatory. In the present invention, the reason set is constructed first, and in the GGNN transient stability evaluation model, the soft attention mechanism is used to output the maximum node score. The node score is the largest, indicating that the node has the greatest relationship with the instability of the power system. Then use each feature of the node to compare with the event set to get the probability of each event, and then output the event with the highest probability. FIG. 14 shows that among the tested samples, the samples that are judged to be unstable are predicted to be the results of the above events. In Figure 14, each blue bar represents the number of unstable samples classified into one of the above events, and the red bar represents the actual number of unstable samples that actually belong to the event type. The vertical axis is the number of samples, and the horizontal axis is the event type. It can be seen from Fig. 14 that the overall accuracy of judging the cause is 94.82%, and the accuracy of the unstable samples labeled as short-circuit events is the highest, which is 100%. The unstable samples labeled as tap events had the lowest accuracy at 95.91%.

When the real-time data is judged to be unstable, the event with the highest probability is finally output. If each cause has the same probability of two or more causes, there is no output. As shown in Figure 14, the total number of predictions is less than the number of unstable samples in the real test set, which means that each classification has the problem of missed judgment. As shown in Table 6, it is the result of judging the cause of unstable samples for the GGNN transient stability evaluation model. It can be seen from the above figures and tables that the GGNN transient stability evaluation model can determine the cause of the instability of the power system after evaluating the instability of the power system, and the overall accuracy rate is 94.82%.

Table 5. The results of the GGNN model to judge the cause

In the present invention, conditional generative adversarial network (CGAN) is used to generate unstable samples to solve the problem of data imbalance. CGAN can not only generate unstable samples, but also can be used to generate unstable samples with unbalanced events, so that the samples can not only achieve a balance between stable and unstable, but also achieve a balance of events in unstable samples. After solving the data imbalance problem of the samples, the GGNN algorithm is used to evaluate the transient stability of the power system, and to determine the reasons for the instability of the power system. Through experiments, it can be seen that using CGAN can effectively and improve the performance of transient stability assessment to solve the data imbalance problem of power system transient stability assessment. GGNN can also quickly and accurately evaluate the transient stability of the power system, and can judge the reasons for the instability of the power system, and can also achieve good performance.

The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (10)

1. The transient stability evaluation method of gate graph neural network based on unbalanced data, is characterized in that, comprises the following steps: S1, collect the stability evaluation data of the power system, the stability evaluation data includes the bus voltage U1 and the operating parameters _of the motor, the operating parameters of the motor include the motor active power P, the motor reactive power Q, the motor voltage Amplitude U, motor current I; S2. Use the transient stability assessment model to realize the stability assessment of the power system. The process of the transient stability assessment model to realize the stability assessment of the power system includes the following steps: Generate a graph G(V, E) based on the stability evaluation data, where V represents the generator set and v∈V, select the generator set as the node v, and e _vw ∈ E is the edge between the nodes v and w; the motor active power P, the motor Reactive power Q, motor voltage amplitude U, motor current I are used to form the annotation vector of nodes, and bus voltage U ₁ is used to generate edges between nodes; Based on the graph G(V,E), first use the first GGNN model to evaluate the transient stable instability state, if the output of the model is the transient stability of the power system, enter the next cycle; otherwise, use the second GGNN model to evaluate and continue Determine the type of events that cause system instability; The first GGNN is a two-class model, and the output is a stable state and an unstable state; the second GGNN model is a multi-class model, and the output is an unstable type, corresponding to determine the cause of the instability of the power system; The transient stability evaluation model is pre-trained, and the training process includes the following steps: The stability evaluation data of the power system is collected as sample data. The operating parameters of the motor in the sample data also include the relative rotor angle δ of each generator. Based on the sample data of the relative rotor angle δ of each generator, the transient stability index is used to The steady state of the power system is divided into stable state and unstable state; Then, for the data in the unstable state, the first CGAN is used to generate unstable samples, and the second CGAN is used to generate unstable samples of different events; A graph G(V, E) is generated using samples from stable states and samples corresponding to unstable states, and trains a first GGNN model for evaluating transient stability and a second CGAN model for evaluating events corresponding to unstable samples. 2. The method for evaluating the transient stability of a gate graph neural network based on unbalanced data according to claim 1, wherein the first GGNN uses a gate recursive unit GRU in the propagation step. 3. The method for evaluating the transient stability of a gate graph neural network based on unbalanced data according to claim 2, wherein the second GGNN uses a gate recursive unit GRU in the propagation step. 4. the gate graph neural network transient stability assessment method based on unbalanced data according to claim 1,2 or 3, is characterized in that, the loss function in the process of training the first GGNN model

where l _i represents the label of sample i, hi represents the graph-level representation vector of sample i, _i represents sample i, and G represents the sample size. 5. the gate graph neural network transient stability assessment method based on unbalanced data according to claim 4, is characterized in that, the propagation recursive process of described first GGNN model is as follows:

in,

Represented as the hidden state of node v at time t, x _v is the node annotation vector of node v; T represents the transpose of the vector;

Node v collects information from neighbor nodes;

A vector represents the information about neighbor nodes collected by node v at time t; A _v is a sub-matrix of the graph adjacency matrix, representing the connection state of node v and its neighbor nodes; V represents the number of nodes;

represents the hidden state of node 1 at time t-1, V represents the number of nodes,

representation vector

The transpose of , b represents the calculation

the vector;

in

represents the updated information of node v at time t,

Represents the information of node v at time t, the matrices W ^z and W ^r are used to calculate the weight matrix of z and r, and the matrices U ^z and U ^r are also used to calculate the weight matrix of z and r; z and r represent the update gate and Reset the gate, σ represents the sigmoid function;

where tanh(x) is the activation function, and ⊙ is the element-wise multiplication operation; When graph-level output, the graph-level representation vector is defined as

in,

acts as a soft attention mechanism that decides which nodes are relevant to the current graph-level task, i and j are the

and x _v are cascaded as input and output real-valued neural network; h _g is used to judge the transient stability of the power system. 6 . The method for evaluating the transient stability of a gate graph neural network based on unbalanced data according to claim 5 , wherein h _g >0.5 of the first GGNN model indicates stability. 7 . 7. The gate graph neural network transient stability assessment method based on unbalanced data according to claim 6, is characterized in that, the loss function in the process of described training the second GGNN model

Among them, l ₁ represents the label of the event type, k represents the number of event types, and a _j is the output of the activation function softmax. 8. The gate graph neural network transient stability evaluation method based on unbalanced data according to claim 7, is characterized in that, before training the first GGNN model and the second CGAN model, for generating the first unstable sample The CGAN and the second CGAN are pre-trained, and the training process includes the following steps: The data data x of CGAN is constructed according to the stability evaluation data of the power system collected as the sample data: x=[x ₁ ,x ₂ ,...,x _n ] (2)

a _i = [U ₁ PQUI δ] _1×89 (4) Among them, n represents the number of input samples, and it can be known from equation (2)(3)(4) that the input data is n arrays of 500*89; The input condition of the discriminator D of CGAN is the label vector of the sample data, which is an n×1 array; Generate multi-label data based on sample data, each data has 2 labels: L={l ₁ ,l ₂ } (5) Among them, l ₁ represents the event that caused the data state, and l ₂ represents the stable state of the system; l ₁ = {0, 1, 2, 3, 4} (6) The event represented by l ₁ =0 is a short circuit event, the event represented by l ₁ =1 is a tap event, the event represented by l ₁ =2 is a load event, the event represented by l ₁ =3 is a switching event, and the event represented by l ₁ =4 The event is a synchronous generator event; l ₂ = {0, 1} (7) When l ₂ is 0, the sample is unstable; when l ₂ is 1, the sample is stable; L is an array with 1 row and 2 columns; Based on the sample data and the corresponding labels, the CGAN model corresponding to the generated unstable samples and the CGAN model corresponding to the unstable samples generated with different events are trained as the first CGAN model and the second CGAN model, respectively. 9. The gate graph neural network transient stability evaluation method based on unbalanced data according to claim 8, characterized in that, in the process of collecting the stability evaluation data of the power system, the fault clearing time is recorded as At time 0, the bus voltage and motor operating parameters are collected according to the time interval of 0.01s. 10. The method for evaluating the transient stability of a gate graph neural network based on unbalanced data according to claim 9, wherein the transient stability index

where _δmax is the maximum relative rotor angle of any two generator sets in the simulation duration.

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