Modelling and Simulation in Engineering

Volume 2018, Article ID 5608591, 12 pages

https://doi.org/10.1155/2018/5608591

## Assessment of Transient Stability through Coherent Machine Identification by Using Least-Square Support Vector Machine

^{1}Department of Electrical Engineering, Malaviya National Institute of Technology, Jaipur, Rajasthan 302017, India^{2}Department of Electrical Engineering, Swami Keshvanand Institute of Technology, Jaipur, Rajasthan 302017, India

Correspondence should be addressed to Bhanu Pratap Soni; moc.liamg@1102inospb.re

Received 23 December 2017; Revised 20 March 2018; Accepted 29 March 2018; Published 10 May 2018

Academic Editor: Elio Chiodo

Copyright © 2018 Bhanu Pratap Soni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Transient stability assessment (TSA) of the power system is a crucial issue with escalating demands and large operational constraints. Real-time TSA allows for deciding and monitoring of the relevant preventive/corrective control actions depending on the dynamic behavior of the system components. To assess this, coherency of generating machines is to be found. After determination of the coherent machines, any corrective or preventive action can be initiated by the system operator to maintain stability of the system during occurrence of any severe contingency. The Transient Severity Index (TSI) introduced in this paper has proven to be an interesting alternative for determining generator coherency. Furthermore, the numerical values of this index are employed to construct a supervised learning-based classifier and the ranking method with the help of system load and generation as input features. This framework employs the support vector machine (SVM) to perform the ranking of the generators based on severity and classify them into vulnerable and nonvulnerable machines. The results are validated on the IEEE 10-generator, 39-bus test (New England) system. It is observed that the proposed index and the supervised learning engine give satisfactory results and both are aligned with the published approaches.

#### 1. Introduction

Modern power network is emerged from the vertically integrated structure to the deregulated unbundled structure. This transformation enables consumers and generators to participate in the competitive business environment. Issues of power quality, reliability, risk, and security become prominent in this environment. High power demand has made an essential criterion to maintain the power system secure under the stressed operating conditions. Transient stability (T/S) of the power system is an important denominator and defined by the CIGRE committee [1] as “the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact.” Stability studies can be subdivided into two categories: the first one is assessment and the second one is control. Ensuring T/S under any unforeseen contingency is a challenge for a system operator. This fact initiated the research in the direction of assessment methods along with preventive control methods for ensuring system stability.

In the past, various methods have been applied by researchers to assess system stability. Stability analysis-oriented research is mainly based on the evaluation of the violation of the limit of power system quantities and the behavior of the generator under contingency conditions. Some methods [2–5] proposed for stability assessment in the latest literature were based on risk or probabilistic, pattern recognition, and time domain simulation (TDS) techniques. TSA is directly concerned about the large disturbance. A risk-based methodology was proposed in [2–4]. A probabilistic small-disturbance stability analysis (PSSA) method with uncertainties was proposed by Preece and Milanović [2]. In this approach, the probability density functions (PDFs) were designed for the damping of the critical oscillatory electromechanical modes by modeling the stochastic variation of system uncertainties. However, this article did not give any analysis for large disturbances. A linear function-based technique was used in [3] to calculate a risk-based index for TSA. A new technique to identify the severity of the power substation under possible operating scenarios was proposed by Da Silva et al. [4]. The research work presented in [5] was based on the pattern discovery-based fuzzy classification. The pattern identification algorithm was modified by using centroid deviation analysis and predisturbance information of the training data set. This centroid deviation analysis-based technique is very difficult for practical implementation. The Lyapunov stability criteria were given in [6] for differential/algebraic models of power systems which include the effect of generator damping and nonlinear loads. Cheung and Chow [7] investigated the simulation of slow dynamics in two-time-scale power systems. In this work, an approach was proposed to obtain the slow dynamics by projecting the trajectory of the postfault system onto its slow manifold. Direct stability analysis of AC/DC power systems using a structure-preserving energy function (SPEF) was proposed in [8]. Bhat et al. [9] gave a concept of the single machine equivalent (SIME) T/S method combined with Simulink to model T/S phenomena and the Graphical User Interface Design Environment (GUIDE) software of MATLAB. A method based on the network decomposition algorithm was presented in [10] to implement simultaneous unbalances in power system T/S.

In the current decade, many researchers have proposed stability indices for assessment of stability of large power systems. Transient security indices determined in [11, 12] can be used to measure the synchronism state of a generating unit. A small signal stability index was proposed in [13] for power network dynamic assessment by employing TDS. The value of this index was calculated by the systems’ eigenvalues using dynamic simulation. Several indices were presented in [14, 15] for TSA. A practical and heuristic index based on T/S in large power systems was proposed in [14] for fast contingency ranking. A didactic procedure based on simulation for T/S of a multimachine power system was proposed in [16]. Some of the techniques presented in the literature were based on the element T/S, angle stability index, frequency stability index, and transient voltage stability index.

As stated, generator coherency has a considerable application in power system operation and control. The sole concept of coherent groups of generators in a power system is the similar behavior of TDS responses of generators, when they are subjected to a perturbation [17]. This is called coherency. In this consideration, generators that have the similar postdisturbance rotor angle or speed variation characteristics are called coherent and are placed in the similar coherent group. Hence, it is required to monitor and examine the relationship or similarity of rotor angle deviation to find the coherent nature of the power system components. The generators’ dynamic response under disturbances can also be recognized by the deviations in phase angles of voltage or/and current phasors of the system.

Several methods have been introduced in the literature for identification of coherent behavior of the generators and classification of them, 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 find the coherency between generators. 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 required computation of the eigenvalues and eigenvectors of the power system [18]. For example, a synchronic modal equivalencing (SME) was proposed [18] for structure-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 coherent groups of generators. For example, several studies have used the rotor trajectory index (RTI) [12], Fourier spectrum [19], or fast Fourier dominant interarea mode [20], principal component analysis [21], independent component analysis [22], hierarchical clustering methods [23, 24], fuzzy c-medoids algorithm [25, 26], wavelet [27], and Hilbert–Huang transform [28] to find coherent generators. Several techniques proposed in literature cannot always be reliable for all applications, such as system protection schemes or remedial action schemes, dynamic equivalencing, and controlled islanding. This maloperation is found due to the degree of coherency between generators or nongenerating buses. This may change for different disturbances at different power system operating conditions.

Generally, real-time TSA is an approach to find the fast and accurate prediction of the system stability status (either stable or unstable) in real time by considering the future behavior of the generator under the disturbed operating condition. In the literature, various topologies were proposed to forecast the system stability states by using different types of artificial intelligence-based techniques [29–32]. Hashiesh et al. proposed a supervised learning technique for T/S state prediction by the artificial neural network (ANN) [30]. The SVM-based techniques [31] were used for power system contingency classification and ranking in [29, 32]. The real-time TSA method using the SVM was also proposed in [33]. The prediction of the real-time transient state of the power can be done successfully by the above-discussed methods, but these methods are used only as a classifier. The stability status of the individual generator for any contingency cannot be determined by these methods. For the control action like generator rescheduling, knowledge of the individual generator state (either stable or unstable) is mandatory. To overcome these deficiencies, we propose an SVM-based method to predict the status of the individual generator and overall system by using the coherent characteristics of the generators.

In this paper, the T/S status of the power system is analyzed by simulating the power system under different operating conditions, on different fault locations, and for different fault clearing times. The status of system stability is identified by using a new index, Transient Severity Index (TSI). This index is based on rotor angle deviation of the generators in the postfault state. A supervised learning engine based on the LS-SVM is proposed to rank the generators according to the values of TSIs. The potential features for this supervised learning engine are extracted from TDS of the power system under dynamic operating conditions. These potential features are real, reactive power at generating and load buses.

The remaining part of this paper is organized as follows: Section 2 describes power system modeling, Section 3 contains the mathematical framework of the proposed TSI along with the model of the LS-SVM. In Section 4, simulation and results are presented, while Section 5 highlights major conclusions drawn from the work and also presents a solid milieu for future work.

#### 2. Power System Modeling

The TDS method is used to solve the differential equations involved in power system stability analysis. TDS of the power system is required for DSA to find whether the system can maintain synchronism during disturbance or not. This decision is taken by monitoring the movement of trajectories of rotor angles during a perturbation period. The swing equation shows the transient behavior of the system. If the trajectories of the rotor angle of either a single generator or a group of generators are found to have continuous increment without limit with reference to remaining machines, then the system is unstable. Another phenomenon is if rotor angles of all working system generators remain bounded within their respective permissible limits, then the system is stable [17, 34]:where is the transfer admittance between the and generators, is the moment of inertia, is the electrical power output, is the damping coefficient, is the mechanical power input, is the rotor speed deviation, is the rotor angle of the machine, and is the rotor angle of the machine. The deviation between generator rotor angles with reference to time can be found by using the set of swing equations (1)–(3):

In the projectile transient phenomena, the inertial center of the system is taken as the reference frame for the calculations. The machines’ rotor angles with respect to center of inertia [35] are used to detect whether the system is stable or not. For an machine system with the inertia constant and rotor angle of the machine, the inertial center is determined as per (4).

#### 3. Proposed Methodology

In this work, a numerical integration technique (Runge–Kutta method) is used to solve the swing equation. The transient security status is determined by monitoring the swing in rotor angle trajectories and deviation in rotor angle with respect to the constraint for transient instability. The constraint is given as follows:where is the maximum allowable value of the relative rotor angle for secure operation. During the case of disturbance, if the relative rotor angle violates in a time interval , then the system is considered as insecure , else it is considered as secure . For this work, the maximum allowable value of the relative rotor angle for secure operation is taken as [36].

The ranking of the generating machines for every insecure contingency needs to be discovered with less computational burden and time. Therefore, the rotor angle trajectory-based severity index, called the Transient Severity Index (TSI), is proposed in this paper. The TSI is determined from TDS, and the process of determination is shown in Figure 1. The TSI can be used to assess the stability of the power system and to rank the criticality of the generators. Hence, it gives the synchronizing condition for a given hard contingency. In this work, we present a method to rank the machines by employing the TSI. Equation (6) shows the mathematical formulation of the TSI:where is the value of rotor angle deviation in degrees, is the trajectory constant, and is the time at which is measured. for all the generators is noted after of fault clearing time (FCT). A classification boundary is shown in Table 1. The numerical value of the TSI is an indicator of the unstable or stable system state of the power system.