Transient stability refers to the ability of power systems to maintain synchronism when subjected to large disturbances (Hatziargyriou et al., 2021). When a power system is at risk of losing the transient stability, if no proper actions are taken, it may cause cascading outages, uncontrolled network splitting, and eventually wide-spread disruption of electricity supply (Andersson et al., 2005). Therefore, maintaining the secure operation of power systems is of great concern to transmission system operators (TSOs). To protect power systems against transient instability, a considerate amount of research efforts has been spent on developing advanced approaches in the field of power engineering.

Online transient stability assessment (TSA) is the first and foremost step for instability prevention as it provides the TSOs with the ability of situation awareness. The conventional method for TSA is the time-domain simulation (TDS) (Kundur et al., 1994). However, TDS is not capable for real-time stability assessment as solving the high-dimensional differential algebraic equations (DAEs) of an interconnected transmission system is computationally burdensome. Also, TDS cannot provide the information on the stability margin and the countermeasures against the unstable scenarios. To address these two drawbacks of the TDS method, transient energy function (TEF) methods (Pai, 1989), also known as direct methods, have been studied since 1980s. By comparing the kinetic energy at the fault clearing time with the critical energy, the stability status and the energy margin can be assessed without the need of simulating the post-fault trajectories by the TDS. While the critical energy is related with the controlling unstable equivalent point (CUEP) (Chiang, 2011), the CUEP of an ongoing fault contingency is usually hard to identify in real-time manner.

Both the TDS and the TEF are model-driven methods for TSA. With the development of phasor measurement units (PMUs), data-driven methods are considered as the prospective alternative to the model-driven methods. Emergency single machine equivalent (E-SIME) approach (Pavella et al., 2000) attempts to compute the energy margin based on the synchronized PMU measurements. But still, the critical unstable mode should be predicted correctly so as to ensure the accuracy of this approach. The maximal Lyapunov exponent (MLE) is proposed in (Dasgupta et al., 2015) to detect the divergence or convergence of the generator rotor angle trajectories. But the MLE may oscillate from positive and negative values before the disturbed power system settles down, which thus requires a sufficiently long monitoring window to avoid the misclassification of stability status. In recent years, encouraged by the success of artificial intelligence (AI) in the fields such as computer vision and nature language processing, AI-based approaches are gaining more attentions.

Machine learning (ML) algorithms including the decision trees (DTs) (Yang et al., 2017; Cremer et al., 2019), support vector machines (SVMs) (Wang et al., 2016; Hu et al., 2019), neural networks (NNs) (AL-Masri et al., 2013; Zheng et al., 2017), and ensemble predictors (Kamwa et al., 2010; Qiu et al., 2019) have been proposed for power system security assessment. The existing literature on this topic can be sorted into two categories, which are Pre-disturbance Stability Assessment and Post-disturbance Stability Assessment, depending on whether the post-disturbance measurement is used as the input features. In this paper, post-disturbance stability assessment is studied. At the early stage of the researches on post-disturbance stability assessment, swallow predictors, such as SVMs and single-layer NNs, are used. Considering that the natural characteristics of power system transient stability is highly nonlinear, feature extraction should be performed before developing the predictor for stability assessment. While some literature adopts the wide-area severity indexes as the input features based on the expects’ experience (Kamwa et al., 2010; Wang et al., 2016), voltage templates-based (Rajapakse et al., 2010) and Shapelet learning-based (Zhu et al., 2016; Zhu and Hill, 2022) feature extraction schemes are proposed to improve the performance of the stability predictors. The emerging deep learning algorithms can be used for representation learning without the need of feature engineering. In (Yu et al., 2018), the long short-term memory (LSTM)-based recurrent learning algorithm is proposed to develop a time-adaptive transient stability framework. In (Zhu et al., 2020), a convolution neural network (CNN)-based hierarchical learning machine is proposed to learn transient temporal correlations for online TSA.

When the impending instability status is detected, remedial actions, also termed as system integrity protection scheme (SIPS), should be implemented to retore the synchronism of the power system. In (Bhui and Senroy, 2017), a look-up table of modes of disturbance is proposed to assist the online computation of the CUEP and the critical energy for TEF methods. Following the E-SIME framework, the pair-wise relative energy function is proposed in (Gou et al., 2017) to identify the critical unstable mode and to design the emergency generation shedding scheme for transient instability prevention. Although AI-based pre-disturbance stability predictors have been widely studied and employed to develop the integrated preventive control schemes, such as (Xu et al., 2012; Liu et al., 2014; Liu et al., 2020), AI-based approaches for emergency control against post-disturbance transient instability are rarely reported to the best of the authors knowledge. The decision trees are used to trigger the controlled islanding (Senroy, 2006) and the power regulation of HVDC intertie (Gao and Rovnyak, 2011). But these control actions are determined by offline analysis. In (Paul et al., 2020), the LSTM network is also used as the instability detector and then the remedial actions are determined by the continual monitoring of the out-of-step generators based on the individual machine transient energy function.

With the ever-increasing penetration of renewable energies, TSOs are facing with greater challenges in protecting power system. On one hand, it is more difficult to implement preventive control due to the inadequate resources for operating condition regulation. On the other hand, the intermittency of renewable energies will inevitably increase the variation of the real-time operating condition, which also make it more difficult to design the fixed system integrity protection scheme, that is, effective for different scenarios. Therefore, response-based SIPS should be developed to address the above-mentioned challenges. This paper attempts to fill the gap between PMU-based post-disturbance transient stability prediction and AI-driven real-time decision making of emergency generation shedding in order to develop an integrated wide-area protection and control scheme. The gated recurrent unit (GRU)-based RNN is proposed as the base predictor. As is discussed, the decision-making for post-disturbance transient stability includes the prediction of the stability status, the unstable mode and the needed amount of generation shedding. Considering that these three predictive targets are basically correlated tasks, a multi-task learning (MTL) framework is proposed. Case studies on the IEEE 39-bus system is presented to demonstrate the effectiveness of the proposed approach.

The rest of this paper is organized as follows. Problem description is provided in Section 2. The gated recurrent units-based recurrent neural network is introduced in Section 3. The multi-task learning scheme for integrated real-time decision-making of transient stability protection is proposed in Section 4. Case studies on the IEEE 39-bus system is presented to illustrate the effectiveness of the proposed scheme in Section 5. Finally, conclusions are drawn in Section 6.

As is discussed, transient stability relates to whether the power system can maintain synchronism when subjected to a large disturbance. The disturbance, such as a short-circuit fault, will lead to the imbalance of the mechanical torque and the electrical torque of each of the generators. Then some of the generators will increase their rotor speed with respect to the others, which forms the accelerating group and the decelerating group of generators. The generator rotor angle trajectories under a fault contingency in the IEEE 39-bus system is shown in Figure 1. As can be seen from Figure 1, the generators {G33, G34, G35, G36} together form the accelerating group, while the rest of generators form the decelerating group.

Based on the idea of center of inertia (COI), the accelerating group and the decelerating group of generators can be reduced to two equivalent machines by Eq. 1: δ S = ∑ i ∈ S M i δ i M S , M S = ∑ i ∈ S M i δ A = ∑ j ∈ A M j δ j M A , M A = ∑ j ∈ A M j . (1)

After the grouping of the generators, the SIngle Machine Equivalent (SIME) can be further determined by Eq. 2: δ = δ S − δ A M = M S M A M S + M A d 2 δ d t 2 = M − 1 P m − P e , (2) where P m = M S + M A − 1 M A ∑ i ∈ S P m i − M S ∑ j ∈ A P m j , (3) P e = M S + M A − 1 M A ∑ i ∈ S P e i − M S ∑ j ∈ A P e j . (4)

After computing the SIME of the multi-machine power system, the conventional equal-area criterion (EAC) can be used to compute the energy margin-based transient stability index (TSI) and to estimate the necessary amount of generation shedding for instability prevention when the system is about to lose synchronism. Figure 2 depicts the EAC criterion (Kundur et al., 1994; Gou et al., 2017). If the decelerating area A _dec is smaller than the accelerating area A _acc, the system will lose synchronism when the operating point travels through the unstable equivalent point (UEP), which refers to the operating point with the equivalent rotor angle to be δ u .

In Figure 2, δ 0 denotes the rotor angle of the SIME at pre-fault condition, δ s is the rotor angle relating with the stable equilibrium point of the post-fault condition, while δ u is the one relating with the unstable equilibrium point of the post-fault condition without generation shedding. δ c is the rotor angle of the SIME at fault clearing time and δ d is the rotor angle of the SIME when generation shedding is implemented. Accordingly, δ u ′ is the rotor angle relating with the unstable equilibrium point after generation shedding. Respectively, P e P r e − f a u l t , P e F a u l t − o n , and P e P o s t − f a u l t denote the mechanical power output of the SIME for pre-fault condition, fault-on condition and post-fault condition. △ P s h e d denotes the amount of generation shedding and A _add is the increased decelerating area caused by generation shedding.

For unstable cases, generation shedding should be implemented to make the SIME decelerates before travelling through the unstable equivalent point. Based on the EAC, the necessary amount of generation shedding P s h e d can be computed by Eq. 5 (Pavella et al., 2000; Gou et al., 2017): P s h e d = A a c c − A d e c δ u ′ − δ d ≈ E K E δ u δ u − δ d = 1 / 2 M ω t u 2 δ u − δ d , (5) where E K E δ u denotes the kinetic energy of the SIME at the UEP. ω is the rotor speed of the SMIE and ω t u denotes the value at the UEP.

The earlier the control decision is made; the less generation shedding is needed. However, for E-SIME method and its derivatives, it is usually difficult to identify the critical unstable mode and the relative UEP. To tackle this problem, this paper tries to make the best of deep learning algorithms, which have the attractive capability of nonlinear representation and real-time decision-making. By learning from the offline generated knowledge base, the deep learning-based predictor not only predict the stability status, but further address the problems including the grouping of unstable generators and the estimation of the amount of generation shedding.

In Section 3, the GRU-based predictor is proposed for post-disturbance transient stability classification. In this section, the predictor is extended for the integrated prediction and control against transient instability by multi-task learning (MTL).

There are a handful of examples of multi-task learning, such as natural language processing (Collobert and Jason, 2008) and computer vision (Girshick, 2015). Although one can handle these tasks in the separated way, i.e., a specific neural network is developed for each task, multi-task learning aims to improve the generalization by leveraging domain-specific information contain in the training signals of related tasks (Ruder, 2017). In practical power systems, there are some transmission interfaces that are correlated in terms of the dominated stability mode. In (Huang et al., 2019), multi-task learning is proposed to train a compact model to evaluate the total transfer capacity (TTC) of these correlated interfaces in the united manner.

The prediction of post-fault stability status, the identification of critical unstable machines, and the estimation of generation shedding are related tasks. Therefore, multi-task learning is used to fulfill the above-mentioned tasks in order to develop the adaptive PMU-based system integrity protection scheme against transient instability. The structure of the multi-task deep neural network is demonstrated in Figure 5. The GRU-based RNN is used to extract the latent features following the basic MTL structure of hard parameter sharing. After extracting the latent features, task-oriented multi-layer perception model are developed to fulfill different tasks. To train the parameters of the multi-task deep neural network, the loss function is defined as is in (11): L = L T S A + ∑ i = 1 N G L G i + L G S , (11) where L T S A = 1 N S ∑ s − y s T S A ⁡ log ⁡ p s T S A + 1 − y s T S A log ⁡ p s T S A , (12) L G i = 1 N S ∑ s − y s G i ⁡ log ⁡ p s G i + 1 − y s G i log ⁡ p s G i , (13) L G S = 1 N S ∑ s y s G S − p s G S 2 . (14)

The subscript s denotes the serial number of a training sample and N S is the total number of training samples. L T S A denotes the cross-entropy loss function for transient stability classification. y s T S A is the label of stability status for the sth sample, while p s T S A is the related prediction. L G i denotes the cross-entropy loss function for the ith generator. y s G i is the label that indicates whether the ith generator belongs to the accelerating group for the sth sample, while p s G i is the related prediction. L G S denotes the mean square error (MSE) for generation shedding estimation. y s G S denotes the amount of generation shedding and is computed by offline SMIE analysis, while p s G S is the related prediction.

The pseudo-code of the training procedure is demonstrated in Algorithm I.

The proposed scheme includes two stages, namely the offline model training stage and the online decision-making stage.

The proposed scheme is illustrated by case study on the IEEE 10-machine 39-bus system (Pai, 1989). The network structure of the testing system is shown in Figure 6. Power flow and time-domain simulation are implemented by using PSD-BPA, which is the power system analysis package developed by the China Electric Power Research Institute (CEPRI). It is assumed that all the generator buses are equipped with PMUs so as to enable post-fault transient stability prediction and real-time decision-making for emergency generation shedding control. Also, all the power plants are assumed to be formed by five identical units that operate in parallel. The maximum number of units that allow to be shed is four so that at least one unit should be connected to the power grid.

To protect power systems from transient instability and the subsequent catastrophic blackouts, an integrated scheme is proposed by using post-disturbance PMU measurements and multi-task deep learning. The GRU-based predictor is firstly proposed for post-disturbance transient stability prediction. On this basis, considering that the prediction of the impending instability, the identification of the unstable mode, and the estimation of generation shedding are essentially related tasks, a multi-task learning framework is proposed to develop the PMU-based system integrity protection scheme for transient stability. Case study on the IEEE 39-bus system demonstrates that, apart from the basic task of transient stability prediction, the proposed multi-task predictor can predict the grouping of generators correctly. Moreover, based on the estimated amount of generation shedding, the generated remedial control actions can retain the synchronism of the power system.

Future research involves two aspects:

1) The proposed scheme is an open-loop SIPS and the overall percentage of success decision-making is 94.40% in the case study on the IEEE 39-bus system. In this regard, future research focuses on developing the close-loop SIPS following this paper so as to further enhance the percentage of success decision-making.