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This paper presents a novel approach to dynamic phasor-based transient stability simulation. The proposed method is based on the modified nodal analysis (MNA) approach to circuit simulation, which is used to construct continuous differential-algebraic equations (DAEs). The proposed method makes use of the stamp technique, which makes it possible to construct a general purpose MNA-based simulator. Stamp-based models for common power system components are derived in this work. A new MNA-based synchronous machine model is presented, which represents machines as nonlinear inductances instead of subtransient equivalents. The resultant continuous DAEs are numerically solved using the general purpose variable step and variable order library \texttt{IDA}. Simulation results from the IEEE 68 bus test system, a real 400 bus power system, and the IEEE 39 bus test system with an embedded HVdc transmission system demonstrate that the proposed method is suitable for large ac networks with power electronic devices. The results demonstrate good agreement between the proposed method and electromagnetic transient (EMT) simulation. The results also demonstrate that the proposed method is fast and scalable with CPU times that are up to 200 times faster than EMT simulation.

The absence of complete model data of a power system hinders complete eigenvalue analysis of that system. System identification methods have been used to identify operating-point-dependent equivalent linear model of a power system. Such identified models do not allow a complete eigenvalue analysis. To resolve this, the identification problem can be formulated in such a way to utilize any a-priori knowledge of the system. Model data of a synchronous machine consists of machine data and controller parameters. Methods to determine synchronous machine parameters are well established. In this paper, knowledge of the machine data and knowledge of eigenvalues of the system at multiple distinct operating points, extracted by a system identification method, are used to determine auxiliary controller parameters of the synchronous machine. Model data that are determined by the proposed method is independent of the operating point. Therefore, it can be easily integrated into a complete small signal stability study at any operating point of the synchronous machine.

More and more system operators are interested in calculating transfer capability in real time using real-time power flow models generated from the Energy Management System (EMS). However, in comparing these models with offline study models, the EMS models usually include only a limited portion of the interconnected system. It is not practical to extend the EMS model in order to capture the impact of the external systems and as such using an equivalent network becomes necessary for this purpose. Equivalent circuits derived from the offline models for certain predetermined operating conditions would suffer from invalid results under various real-time operating conditions. Hence, it is necessary to derive an equivalent circuit model that is adaptive to the real-time system conditions. This paper presents a general method of creating an equivalent circuit model based on the measured boundary station parameters such as voltages and power flows. Simulation studies show that such derived equivalent circuit models provide solutions with adequate accuracy.

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation.

This paper introduces a screening method to determine the potential risk of interactions between a dynamic device and a generator with torsional oscillations. The proposed method introduces a factor called the radiality factor (RF) which is an indicator of the radialness of the network between the device and the generator. The RF is calculated in the sub-synchronous frequency range and plotted against the frequency (RF curves). The RF curves can then be used for screening of torsional interactions between the generator and other dynamic devices. The critical value for the RF is determined through a large number of sensitivity studies on a test system. This method surpasses the available screening method: unit interaction factor (UIF) calculations which is only applicable for inductive networks without series compensated lines.

This paper proposes a robust frequency-domain method to tune the $d$ – $q$ decoupled control system used in Modular Multilevel Converter-type Voltage Source Converter (MMC-VSC) systems. A linearized state-space model of the MMC-VSC system is developed and used to calculate the stability-related frequency-domain attributes. The controller design problem is formulated as an optimization problem. In this paper, the simulated annealing optimization technique is applied to find the proportional-integral (PI) controller parameters that give desired damping for the oscillatory modes and desired values for decaying exponential modes. The efficacy of this method is tested on the electromagnetic transient model of a two-terminal MMC-VSC system on the real-time digital simulators, and the results are provided in this paper. Finally, tuned controller parameters for different ac system strengths are discussed and it is shown that this mathematical model is suitable to tune the PI-controller parameters for MMC-VSC systems connected to strong as well as weak ac networks.

This paper presents a novel approach to enable frequent computational cycles in online dynamic security assessment by using the terms of the transient energy function (TEF) as input features to a machine learning algorithm. The aim is to train a single classifier that is capable of classifying stable and unstable operating points independent of the contingency. The network is trained based on the current system topology and the loading conditions. The potential of the proposed approach is demonstrated with the New England 39-bus test power system model using the support vector machine as the machine learning technique. It is shown that the classifier can be trained using a small set of data when the terms of the TEF are used as input features. The prediction accuracy of the proposed scheme was tested under the balanced and unbalanced faults with the presence of voltage sensitive and dynamic loads for different operating points.

This paper utilizes a class of modern machine learning methods for estimating a transient stability boundary that is viewed as a function of power system variables. The simultaneous variable selection and estimation approach is employed yielding a substantially reduced complexity transient stability boundary model. The model is easily interpretable and yet possesses a stronger prediction power than techniques known in the power engineering literature so far. The accuracy of our methods is demonstrated using a 470-bus system.

Summary form only given. This paper presents a comprehensive analysis of sub-synchronous interactions in a wind integrated power system to understand and mitigate them. The proposed procedure has two steps. In the first step, a frequency scan is performed to determine the presence of resonant frequencies in the sub-synchronous range. In the second step, a detailed small signal analysis is performed. Participation factors are used to identify the state variables that are involved in the interaction, and the controllability indices are used to determine the mitigation method. It is shown that the sub-synchronous interaction present in Type 3 wind turbine-generators connected to the grid through series compensated lines is an electrical resonance between the generator and the series compensated line which is highly sensitive to the rotor side converter current controller gains.

This paper presents a brief review of techniques available for reducing large systems to smaller equivalents. This paper is divided into high frequency equivalents, low frequency equivalents, and wideband equivalents. Numerical examples are presented to demonstrate selected methods of high frequency equivalencing.

This paper presents a linearized technique to determine a risk-based index for dynamic security. The method is an extension to an existing technique in which the risk of steady state security is calculated using the mean and variance of load uncertainty. The proposed method is applied to calculate the risk indices for the IEEE New England 39-bus test system. The results obtained from the proposed method are validated against those estimated by Monte Carlo simulation. Both approaches produce virtually the same results for small load deviations.

The paper discusses the dynamic behavior of two different flexible ac transmission system devices; the interline power-flow controller (IPFC) and the unified power-flow controller (UPFC) in a benchmark system. The small-signal model of the interline power-flow controller is developed and validated using detailed electromagnetic transients simulation. Using this validated model, the damping capabilities of the IPFC and the UPFC are compared and rationalized. From a small-signal dynamics point of view, it is shown that the series branches of these devices essentially segment the network creating a new structure. This structure change may be used to effectively improve system damping without requiring the design of a tuned feedback controller. The IPFCs two series branches in contrast to the UPFC's single series branch permit more opportunities for network segmentation. Hence, the IPFC has greater potential for improving the system's dynamic performance.

In this paper, an artificial neural network (ANN) based method is developed for quickly estimating the long-term voltage stability margin. The investigation presented in the paper showed that node voltage magnitudes and the phase angles are the best predictors of voltage stability margin. Further, the paper shows that the proposed ANN based method can successfully estimate the voltage stability margin not only under normal operation but also under N-1 contingency situations. If the voltage magnitudes and phase angles are obtained in real-time from phasor measurement units (PMUs) using the proposed method, the voltage stability margin can be estimated in real time and used for initiating stability control actions. Finally, a suboptimal approach to determine the best locations for PMUs is presented. Numerical examples of the proposed techniques are presented using the New England 39-bus test system and a practical power system which consists of 1844 buses, 746 load buses, and 302 generator buses.

The paper applies the method of eigenstructure assignment for the design of a controller for a wind generation scenario in Northern Scotland based on doubly-fed induction generators (DFIGs). The designed controller serves the combined purpose of a conventional power system stabilizer (PSS) and an active damping controller and provides a contribution to both network and shaft damping. This novel approach is superior because all available degrees of freedom are fully exploited by selecting not only the new eigenvalue locations but also certain elements of the left eigenvectors. These elements are obtained by solving a multiobjective nonlinear optimization problem (MONLOP). Examples are presented to demonstrate that optimizing the eigenvectors yields a better performing controller in comparison with one designed using mere eigenvalue relocation.

This paper presents an analysis of multi infeed high-voltage dc (HVDC) interactions using small-signal analysis techniques. The modeling details that are necessary to adequately represent the dynamics of the HVDC converters and the ac network are investigated, and the models are validated against an Electromagnetic Transient Simulation program. The paper shows that ac network dynamics must be modeled in order to obtain meaningful results from the small-signal stability study. A small test system with two HVDC infeeds is then used to demonstrate the presence of interactions in that system. The case studies presented in this paper indicate that it is possible to have interactions between the HVDC terminals in an ac system. This paper recommends that a small-signal interaction study, which is similar to what is presented in this paper, should be performed to identify these interactions.

This paper presents an efficient method to estimate a transient stability boundary (TSB) as a nonlinear function of power system variables. The proposed method exploits the computational efficiency of linear estimation methods to determine an accurate nonlinear function. The novelty of the proposed method is that a nonlinear transformation is applied to the original variables, voltage magnitudes, and phase angles, so that the TSB is approximately linear in terms of the transformed variables. The linear function obtained using the transformed variables is indeed nonlinear in terms of original variables. The attractiveness of this method is that the estimated function is not a linearized approximation, although a linear estimation method is used. The potential of the proposed method is demonstrated using the New England 39-bus system and a larger power system with 470 buses

The paper presents a platform system for the incorporation of flexible ac transmission systems (FACTS) devices. The platform permits detailed electromagnetic transients simulation as it is of manageable size. It manifests some of the common problems for which FACTS devices are used such as congestion management, stability improvement, and voltage support. The platform can be valuable for the validation of reduced order models such as small signal or transient stability models. The paper presents details on the development and validation of a small signal based model with the inclusion of a Unified Power Flow Controller. The validated model is then used successfully for the design of a feedback controller for improved damping.

This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.

In second-order normal form (NF) analysis, the nonlinear dynamical system being analyzed is modeled with nonlinearities up to second order. Due to the presence of nonlinearities in the model, the results of second order NF analysis are initial condition dependent , . There are two assumptions in the theory of NF analysis and in this paper it has been shown that if the initial condition chosen do not satisfy these two main assumptions, then NF analysis is inaccurate. This paper also proposes three criteria to identify whether the initial condition satisfies one of the assumptions or not. This paper proposes to use a snap shot of state variables at an instant subsequent to the clearing of disturbance in situations where the state variables immediately after clearing the disturbance is not suitable for NF analysis. The time-domain simulations are presented to support the analysis.

A hysteresis model based on the Jiles-Atherton theory is incorporated into a power transformer model in an electromagnetic transient program (EMTP)-type program. The eddy current effects are also included in the same model. Comparisons are made between recorded and simulated waveforms using a single-phase distribution transformer. A good agreement is achieved between recorded and simulated data.

The hysteresis loop of the core material in a test current transformer is simulated using the Jiles-Atherton theory. Comparisons are made between recorded and simulated waveforms and it is found necessary to replace the modified Langevin function used by Jiles and Atherton. Using an alternative function described in the paper, good agreement is achieved between test and simulated waveforms.

Design of a fuzzy logic controller needs qualitative knowledge about the system under consideration. This knowledge is usually obtained from experienced human controllers, or using analytical/heuristical techniques. However, with large/complex interconnected power systems, it is extremely difficult to obtain the necessary knowledge from human controllers or using conventional analytical/heuristical techniques. An approach to ascertain the relationships among variables to generate fuzzy rules is presented in this paper. The proposed method is based on system response to pulse input signals applied at appropriate instances. Use of this approach, along with sequential decentralised control design techniques for developing DC current and generator excitation modulation controllers to improve damping of oscillations in an AC-DC interconnected power systems, is presented in this paper. Simulation results reveal the successful application of the proposed rule base derivation approach along with sequential decentralised control techniques to design fuzzy logic modulation controllers for damping improvement of power systems.

W.C. Kotheimer comments on the paper by U.D. Annakkage et al. (see ibid., vol.15, no.1, p.57-61, 2000). The author points out that the original authors have identified an apparent limitation of the Jiles-Atherton algorithm using the Langevin function when used to model the core of a current transformer subjected to high fault currents in the presence of a significant amount of remanence. The original authors reply to the comments.