For the reliable operation of power system, transient stability is the prime concern of the power system operator. The transient or large disturbance rotor angle stability is defined as the ability of the system to remain in synchronism immediately after large disturbance (such as loss of transmission line or generator) [33, 35]. Generally after large disturbance rotor angle of all the generators makes excursion from their pre-disturbance values, if the rotor angles increase/decrease monotonically without bound system is termed as transient by unstable; if however they oscillate between predefined threshold values the system is said to be transiently stable.
2.2.1 Online Transient Stability Assessment
For online assessment of the transient stability various methods have been reported in the literature, which are used for both offline and onlne purposes. These meth- ods include Time Domain Simulation (TDS) [96–103, 157] based approaches, direct methods which are based on the energy functions [35,38,104–106,158–165]and ANN, SVM & Decision Tree (DT) based AI methods and other hybrid methods.
2.2.1.1 Time Domain Simulation (TDS) Methods
The dynamics of the rotation of the generator rotor is governed by the set of non- linear differential equations. The rotor angles of the machines can be explained as a function of time and their values can be obtained by solving these equations by numerical differential techniques such as trapezoidal method for pre-fault, during fault and post-fault periods [96–103,157]. It also provides the information of the state variables in steady state as well during transient period. The rotor angles obtained through numerical integration indicates the transient stability of the system. This is the most accurate and flexible method with respect to modelling of the power system, detailed model of power system can be considered for determining the rotor angles in the post-disturbance scenario [97]. However due to high computational burden, these methods are utilized for off-line purposes rather than for online applications. These methods does not provide information regarding the degree of instability/stability.
2.2.1.2 Direct Methods
The direct methods for stability analysis of power systems are based on the Lya- punov’s stability criterion. These methods have not need to solving the system dif- ferential equations. Thus are computationally efficient but have limited to system modeling capability. These methods are generally based either on Lyapunov’s second method [166] or Equal Area Criterion (EAC) [103,167]. The direct method based on Lyapunov function consists of defining in the state space a region of asymptotic sta- bility for post fault stable equilibrium point and calculating the value of Lyapunov function. Stability is determined by comparing this value with agiven limit value.
Lyapunov function used in the transient stability studies are functions of the energy type known as Transient Energy Function (TEF) [104–106, 158–165]. However, it is difficult to construct a suitable Lyapunov function for multi-machine power system.
The EAC has also been applied as direct method for finding the transient stability state of the system [168]. The problem in implementing energy based methods for online security analysis is, difficulty in finding the function that defines the transient energy of the system. Time response of the state variable can not be obtained with these methods.
2.2.1.3 AI based Method
In recent years various AI based methods like Artificial Neural Network (ANN), Decision Tree (DT), Support Vector Machine (SVM), have been employed in the literature for evaluating the stability of the power system. Due to the capability in handling long series and large data satisfactorily and efficiently, AI based techniques were employed for the stability assessment. The developed methods have the human like learning capabilities and can map the complex input and output. The methods are developed to build classifier for the unseen scenarios for online application. In 1988, application of Artificial Neural Net (ANN) was first proposed for dynamic stability assessment of power system [91]. In [112–115, 169] Feed Forward Neural Network (FFNN) and MLP neural network based methods for Transient Stability Assessment (TSA) were proposed. Fisher discrimination as feature selection based neural network [170] was proposed for power system security assessment. Proba- bilistic Neural Network (PNN) [171–173] used as a classifier for evaluating transient stability. TSA of a single machine infinite bus using multi layer artificial neural network was presented in [174]. In [175] authors investigated the estimation of rotor angles of generators using ANNs and local PMU-based quantities for transient stabil- ity prediction. A method for prediction of generators’ angles and angular velocities for TSA of multimachine power system was proposed using recurrent ANN [176].
Application of MLP ANNs in power system stability assessment using transient en- ergy function was studied in [177]. For monitoring TSA considering system topology changes, multilayer FFNN trained with back propagation algorithm was investigated in [178]. The Critical Clearing Time (CCT) was used as an indicator for evaluation of system transient stability. In [179], authors investigated TSA of a power system using committee neural networks.
2.2.1.4 Hybrid and Other Methods
Hybrid neural network composed of Kohonen network and several radial basis net- works [180] were used for assessing transient stability online. In [76, 181, 182] fuzzy logic and neural nets were used together for dynamic security assessment. In [171, 183,184] different SVM based techniques were proposed for evaluating transient sta- bility of power systems. Transient security assessment was accomplished by Kernel
ridge regression based method [185] using multivariate polynomial approximation. A DT based approach was presented in [186] for Dynamic Stability Assessment (DSA) and load shedding scheme was suggested for enhancing the dynamic performance.
An online DSA [187] scheme using decision tree and phasor measurements was pro- posed, DTs provide online security assessment and preventive control strategy based on real time measurements through PMUs. Haque et al. [188] determined the first swing stability limit of multi-machine power system through Taylor series expansion.
An online methodology was proposed in [189] for assessing the robustness of a power system from the point of view of transient stability, and a scalar transient stability index was derived. In [190], authors investigated the probabilistic transient stability assessment for online application using corrected transient energy margin. Ernst at al. [191] proposed a unified contingency Filtering, Ranking and Assessment ap- proach (FILTRA) that relies on Single Machine Equivalent (SIME) in power system transient stability studies.
2.2.2 Coherency Identification
In the case of disturbance in a multi-machine power system, some of the machines have similar responses, meaning that the difference between their swing curves is so small that they can be considered to oscillate together in a coherent way. Coherency between generators is also an major aspect in dynamic performance of power sys- tems, which has several applications including dynamic reduction of power systems and commissioning emergency safety an d govern strategies. Coherency based several methods have been proposed in literature for dynamic size reduction of power sys- tems. These methods employing slow coherency concept [192], relation factor [193], Krylov subspace methods [194], Synchrony based algorithms [195–197] and applied on different small and large systems.
Many authors proposed methods [197–211] in the literature for identification of coherent behavior of generators and their classification, according to their similar behavior (TDS characteristics). After identification of the coherent groups, control strategies can be applied on them. In order to initiate any preventive control under stressed condition, it is desirable to discover the coherency between generators [198].
In general, coherency classification techniques can be divided mainly into two types.
The techniques that are placed in the first type are based on model reduction and require computation of the eigenvalues and eigenvectors of power system [197]. For example, a Synchronic Modal Equivalencing (SME) was proposed in [197] for struc- ture preserving dynamic equivalencing of large power system models. Techniques that are placed in the second type are based on disturbances and use TDS to find co- herent groups of generators. For example, several studies have used rotor trajectory index [199], Fourier spectrum [200] or fast Fourier dominant inter-area mode [201], principal component analysis [202], independent component analysis [203], hierarchi- cal clustering methods [204–207], Fuzzy c-medoids algorithm [208,209], wavelet [210], and Hilbert-Huang transform [211] to identify coherent generators.
2.2.3 Critical Review
After the power system static security assessment, another most important aspect of the power system is TSA of the power system. Online TSA poses a great challenge for the power system operator under continuous changing system topology. The TDS and energy based direct methods are traditional methods for TSA. The TDS methods are computationally demanding for online applications even though they are more accurate. Also they require exact information about the topological changes which is cumbersome task for present day complex power systems. Employment of energy function based approaches enables the system operator with the information about degree of stability. In the existing TSA indices based methods, no effort has been made to obtain the relative stability of each machine with respect to COI. It is therefore necessary to analyze individual machine trajectory that carries important information on power system dynamic performance. Moreover, these approaches are fast and provide important information for selecting appropriate preventive control strategy. The major difficulty in energy function based approaches is that they are applicable only for first swing instability. Therefore due to the limitations of these methods, from the last three decades there has been rising interests in application of artificial intelligence and machine learning based methods for various power system problems, which are promising for online applications. The methods reported in the literature are fairly accurate and fast but applicable for fixed system topology only. Moreover in these methods emphasis has been on getting results with better accuracy i.e. whether the system is correctly classified as stable/unstable. However
finding the severity of the disturbance is also desirable in addition to accuracy for unstable operating scenarios.
For the control operation there is a need to identify the critical machine and non-critical machines which can effectively participate in the generator reschedul- ing during the unstable state of the system to ensure stable system operation. In large power systems, generally the information about coherency of generators can be effectively used to decide the participating generators for rescheduling to improve the transient stability of power systems. Usually methods discussed in literature for coherency identification generally require extensive calculation. Therefore fur- ther investigations are required for ANN applications in finding relative stability of each generator rather than finding the overall system stability as well as coherency identification for stable power system operation and control.