Multi-task Transient Contingency Screening with Temporal Graph Convolutional Network in Power Systems

Rapid transient stability assessment (TSA) is an essential requirement for power system security. In real-world applications, transient contingency screening (TCS) applies TSA approaches to address the pre-defined contingency sets under online operation conditions. TSA by time domain simulation (TDS) is time-consuming, hence we propose a high-speed temporal graph convolutional network (TGCN) that achieves TSA decisions such that a large-scale contingency set can be scanned quickly with enough precision. Based on multi-graph inputs to reflect the transient process, the TGCN utilizes the graph convolutional network (GCN) to extract topology representations and temporal convolution (TC) layers to encode temporal relations. After above graph embedding, two downstream networks are designed for stability classification and critical generator prediction, respectively. Test results on IEEE 39 Bus system demonstrate its superiority over existing models under different operation topologies, fault locations and clearing modes.


Introduction
During daily operation in power system, the increasing expansion of interconnected grids and the largescale penetration of low-inertia renewable energy cause more stressed operation conditions. To capture the risks owing to the changeable conditions, transient stability assessment (TSA) provides an early warning as well as guidance for pre-fault prevention control. It is triggered every 15min to screen the pre-defined contingency set in real-world power systems, which is named transient contingency screening (TCS) in this paper with the aim of implementing TSA on very large contingency sets. Conventional TSA depends on time domain simulation (TDS) [1], which is time-consuming and difficult to handle increasingly complex power system models in real time operation. Data-driven machine learning (ML) benefits from flexibility, fast speed and its ability to predict stability margins such that it serves as a supplement to the TDS. The application of shallow networks has drawn wide attention, while they need manual feature selection and suffer from poor generalization [2]. To deal with the information loss, major researchers have to feed the models with post-fault dynamics. In recent years, deep learning (DL) methods characterized by high-performance computing and big data are introduced in TSA. On one hand, stacked auto encoder (SAE) [3] and long short term memory (LSTM) [4][5] automatically reduces the overfitting risk of the model through pre-training and temporal  [6][7] avoids significant parameter increases via convolution kernels of space sharing, which allows its ability to face large-scale inputs. Their advantage of automatic feature aggregation reduces the time span covered by the dynamic information to the moment of fault clearance. However, preset TDS for the dynamics is still a bottleneck for the speed enhancement, unless they acquire more information from the operation topologies to reflect the changes of operation conditions or fault locations. Regarding that the power system can be treated as a graph when buses are denoted as nodes and transmission lines are denoted as edges [8]. A natural solution complementary to the gap is the graph learning approaches [9]. More recently, graph convolutional networks (GCNs) are reported in power system applications, such as fault location prediction, load shedding decision and missing data recovery [10][11][12]. Huang et al. [13] verify the effectiveness of GCN in topology learning for multiple TSA tasks. Therefore, we follow GCN and propose a temporal graph convolutional network (TGCN) to fulfill two TCS tasks, i.e. stability classification as well as critical generator prediction. The design objective is that a well-trained TGCN can cover various operation topologies, fault locations. A temporal convolution (TC) module help capture the time-evolving nature of the transient process. The main contributions are summarized a follows: 1) Our model can make TSA decisions only based on the electrical variables at steady-state (t 0-) and the fault occurrence (t0 + ) with the fault information.
2) The multi-task TGCN model can fulfill both stability category and critical generator prediction under the scenarios with different fault locations, operation topologies and clearing modes (i.e., a fault cleared with or without line tripping). Figure 1. The structure of TGCN. As figure 1, the whole TGCN contains graph embedding and downstream networks. Three graphs concerning the transient process are required before the representations are captured by utilizing GCN and TC iteratively. Two multilayer perceptron (MLP), the stability category predictor (SCP) and critical generator predictor (CGP) transform these expressive representations into task-specific outputs. Assume the superscript "l" as the times a graph passes GCN and TC while the subscript "m" as the graph index.

Graph Convolutional network(GCN)
As figure 2(a), CNN performs neighborhood aggregating on inputs that typically denote images or signals in Euclidean space, which are difficult in addressing graph data attributed to the irregularity of node connections. By contrast, graph convolutional filters in figure 2  denotes the parameter matrix, while the scaling parameters ( ) l s W guarantee the consistency of the inputs and outputs.

Temporal Convolution(TC)
To encode the temporal correlation, we introduce a temporal convolution that works on the same nodes in different graphs. For the i th nodes, the inter-graph propagation is as where the convolved feature

Downstream networks
Denote the outputs of SCP as SCp z . It is addressed by the "softmax" operation as where SCP i c  is the confidence of the i th category.

Multi-graph Inputs and Their Labels
The element ( , )  Let N G denote the number of generators, then we define G as the set of generators and G N  c  is a binary vector that denotes the stability of all the generators. The status of a generator i is expressed as: where i   is the absolute value of separation between generator i and the reference generator during the simulation time. The set of critical generators is a subset of G and in particular, c G is an empty set if and only if the system is transient stable.

Loss Functions
The loss function  contains the functions for SCP, CGP and a regularization item Here SCP  is the cross-entropy function for binary classification c c   denotes the confidence of the b th sample on the training set whose total number is B. CGP  is the cross-entropy function for multi-label classification as ( log (1 )log (1  )) The optimization object is to minimize the constraints in (8). During the optimization, the the learnable parameters of GCN, TC layers as well as SCP and CGP are adjusted.

Performance Metrics
The specific metrics for the SCP involve accuracy (ACC), alarm (MA) rate and false alarm (FA) rate.
Considering that CGP predicts the set of critical generators, we introduce the Jaccard similarity to calculate the distance between the sets. Given any two sets , i j  s s  , Jaccard similarity is defined as:

Test System and Model Settings
The studies on proposed scheme is conducted on the IEEE 39 Bus system with 39 buses, 10 generators, 19 loads and 46 transmission lines [13]. The operation states with all transmission lines on service are "Base" cases, while the "N-1" and "N-2" cases are generated by randomly switching off transmission line(s). Besides, the loads are changed based on the basic load level (from 75% to 120%). Set threephase faults at either end of any transmission lines and clear the faulted line with or without tripping after 0.1s. The stability labels are calculated during TDS of 4s. The "Base" and "N-1" cases form the training set (60%), while the "N-2" cases form the validation (20%) and test set (20%). The best model settings are shown in figure 1.

Verification of TC Layer
In this subsection, we compared the proposed model with one without TC layer. As figure 4 shows, the TC layer enables higher accuracy in both tasks, where more improvement is observed in the critical generator prediction, almost 0.9% in JACC. It means the expressive temporal representations can help the model deal with the fine-grained task. The efficiency of a model is also a key factor to be considered. We list the training and inference time in table 2. Obviously, our model exploits the parameter sharing mechanism such that the optimization time consumption is relatively low within 4min. The online inference is far more satisfactory in contrast with TDS. The former finishes a batch in 0.1s whereas the latter needs over 6min. This validates the superior efficiency of our model over TDS in real-time TCS tasks.

Conclusion
In this paper, we introduce a TGCN scheme to address two TCS tasks, stability classification and critical generator predictions based on merely electrical information at t 0-and t 0+ . The popular GCN approach is utilized to achieve graph learning, while a new TC layer aims at encoding the time-evolving nature of the transient process. Two downstream networks share the same graph embedding module and make inference parallelly. Test results on the IEEE 39 Bus system demonstrate the outstanding performance of TGCN in scenarios with different topology disturbances, fault locations or even clearing modes.