1 Introduction 2 Electromagnetic Transients 3 Synchronous Machine Modeling 4 Synchronous Machine Control Models 5 Single-Machine Dynamic Models 6 Multimachine Dynamic Models 7 Multimachine Simulation 8 Small-Signal Stability 9 Energy Function Methods Appendix A: Integral Manifolds for Model Bibliography Index

Power System Dynamics and Stability

Transient stability analysis of a power system is concerned with the system's ability to remain in synchronism following a disturbance In utility planning, transient stability is studied by numerical simulation The long CPU run times for simulation preclude their use for on-line security analysis Interest has therefore shifted toward the Lyapunov direct method of stability analysis This paper provides a critical review of research on direct methods since 1970 Considerable progress has been made on both theoretical properties of energy functions and on criteria suitable for on-line implementation Current theory provides a satisfactory treatment of voltage-dependent reactive power demand, transfer conductances, and flux decay However, it cannot incorporate the exciter control Proposed on-line criteria appear to work very well on sample examples; but, they still lack rigorous justification Finally, recent work has shown that power systems can exhibit chaotic behavior This surprising fact demonstrates that our understanding of the dynamics of power systems remains incomplete

Direct methods for transient stability analysis of power systems: Recent results

In this paper, an online power system transient stability assessment (TSA) problem is mapped as a two-class classification problem and a novel data mining algorithm the core vector machine (CVM) is proposed to solve the problem based on phasor measurement units (PMUs) big data. First of all, an offline training, online application framework is proposed, which contained four sub-steps, namely features selection, offline training, online application, and assessment evaluation. First, 24 features are selected to present the system status. Then in the offline training procedure, the PMU big data is generated by time domain simulation, and a CVM model is trained and tested. In the online application procedure, an interface between PMU data center and feature calculation program is set up to collect real time specific PMU big data and the CVM trained is applied to the TSA problem. Last but not least, the evaluation indices are calculated. Compared with other support vector machines, the proposed CVM based assessment algorithm has the higher precision, meanwhile, it has the least time consumption and space complexity. As long as online PMU big data are received, TSA can be done simultaneously. Case studies on the IEEE New England 39-bus system, and real systems in China and the U.S., exhibit the speed and effectiveness of the proposed algorithm.

Power System Transient Stability Assessment Based on Big Data and the Core Vector Machine

A theoretical foundation is provided for the potential energy boundary surface (PEBS) method for power system transient stability analysis. First, a theory of stability boundaries for two classes of dynamical systems: generalized gradient systems and systems described by a second-order vector differential equation. A complete characterization of the stability boundaries of these two dynamical system classes is given, and a qualitative analysis is conducted of the stability boundary when the vector field of the system is under a certain kind of perturbation. Using these results, the PEBS method is evaluated. Conditions under which the PEBS method gives good stability assessments are derived. A modified PEBS method is suggested. >

Foundations of the potential energy boundary surface method for power system transient stability analysis

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.

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Application of Energy-Based Power System Features for Dynamic Security Assessment

In this paper, a method for reducing computation memory required by Lyapunov' s direct method has been presented. This requirement gets critical when the direct method is applied to transient stability studies of large-scale power systems containing more than 100 generators. Firstly, the system equations, the Lyapunov function, and the linear equations associated with the calculation of the stable equilibrium state, have been formulated in such way that the extreme sparcity of the network admittance matrix could be taken advantage of. Secondly, the programming techniques such as optimally ordered triangular factorization and efficient storage scheme of sparse matrices have been introduced. Lastly, the effectiveness of the method has been investigated with the 107-generator and 363-bus power system represented by the detail generator model including automatic voltage regulators ard power system stabilizers.

Transient Stability Analysis of Large-Scale Power System by Lyapunov's Direct Method

A thyristor-controlled series capacitor (TCSC) substantially improves transmission capacity. It also mitigates subsynchronous resonance (SSR) accompanying conventional series capacitors. With an appropriate angle of thyristor firing, electrical damping becomes almost zero, which is called SSR neutral. This quality comes from TCSC itself. However, negative damping still remains, and is large for firing angle 170/spl sim/180/spl deg/ where little current flows through thyristors. This paper deals with control of firing angle. First, we oscillate the firing angle at a given frequency, and present an analytical method of calculating electrical damping. Next, we show that the damping improves at all frequencies if the firing angle oscillation is in phase with that of rotor angle. Synchronizing torque decreases, however, so a limit must be put on the control gain. Lastly, we execute numerical simulations to verify our analytical results.

/pdf/subsynchronous-resonance-damping-control-of-thyristor-2ysqi6z6yt.pdf

Subsynchronous resonance damping control of thyristor-controlled series capacitor

A combined cycle power plant which combines a gas turbine and a steam turbine can achieve high energy efficiency. Many combined cycle plants have been installed worldwide. However, a large-scale blackout due to combined cycle chain trip-out occurred in Malaysia in 1996. The cause of this chain trip was considered to be a large drop of system frequency. Thus, there is a need to investigate the stability of the combined cycle power plant for the frequency drop. Several dynamic models of a combined cycle plant have been proposed. In our analysis, we use some of them and build a model for a single-shaft combined cycle plant. We execute numerical simulations to see how the combined cycle plant behaves when the system frequency drops. The cause and the countermeasure of the combined cycle plant trip-out are explained. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(3): 9–19, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10117

https://onlinelibrary.wiley.com/doi/pdf/10.1002/eej.10117

Dynamic behavior of a combined cycle power plant in the presence of a frequency drop

Instability of Low-Frequency Oscillation in Longitudinal Power System due to Autoparametric Resonance

The photovoltaic (PV) generator changes its power output with the weather. If the PV output changes fast, the power system may require more load-following capability and spinning-reserve. This paper proposes a method of controlling the change rate of the PV output. The PV generator is combined with an electric double layer capacitor (EDLC). The moving average is used to eliminate short period fluctuations of the PV output. The output of the power conversion system (PCS) is determined by the moving average. The output changes within a limited rate. The capacitor voltage is maintained at a constant value to make the capacitor as small as possible. The necessary capacitance is theoretically derived. The effectiveness of this method is verified by the experiment.

Naoto Kakimoto

Papers

Transient Stability Analysis of Large-Scale Power System by Lyapunov's Direct Method

Subsynchronous resonance damping control of thyristor-controlled series capacitor

Dynamic behavior of a combined cycle power plant in the presence of a frequency drop

Instability of Low-Frequency Oscillation in Longitudinal Power System due to Autoparametric Resonance

Change Rate Control of Photovoltaic Generation Output and Calculation of Necessary Capacitance