This paper presents a novel methodology for the construction of a transient stability boundary (TSB) that overcomes the lack of TSB analytical description for multiple operating states and contingencies in power systems. The proposed approach models the TSB as a nonlinear mapping between the system parameters of interest and the corresponding critical clearing time (CCT). This compact mathematical expression is built based on an efficient discriminative network, broad learning system (BLS). While keeping a high accuracy and generalization ability, the newly introduced construction method provides an efficient update strategy that does not require an entire retraining cycle. These properties make this method suitable for online transient stability assessment (TSA). The prospects of the developed method are verified via case studies by employing the IEEE 9-bus, IEEE 39-bus (New England) test systems and a real system of China Southern Power Grid. In comparison with existing methods, the newly introduced algorithm has a higher prediction accuracy and improved robustness. The demonstrated characteristics indicate that the proposed method may serve as a valuable tool in the framework of online TSA.

This paper presents a comprehensive analysis of the impact that supplementary power control of an HVDC link has on the electromechanical dynamics of power systems. The presented work addresses an interesting phenomenon that may occur when an HVDC power controller is installed to support frequency stability. In specific cases, a high gain HVDC frequency controller could deteriorate system damping. The given analytical study is the first of its kind that addresses this issue by including both: (i) the important higher-order generator dynamics that affect small signal stability simultaneously with an HVDC control as well as (ii) the available local angle/frequency input signals of the controller. The methodological approach here analytically formulates the impact an HVDC control has on the single generator dynamics. Furthermore, the relationship between the damping/synchronizing coefficients and the HVDC gain is explicitly derived when a frequency proportional HVDC controller is installed. The derived expressions confirm that, indeed, there is an optimal HVDC gain with respect to the damping coefficient and a typically positive impact of the HVDC controller on the synchronizing component. Finally, the developed theoretical foundation is demonstrated by the tools of linear and nonlinear analysis in a one-machine system case study.

This paper proposes a data-driven methodology for transient stability assessment (TSA) based on constructing a transient stability boundary (TSB). Without stacking the network layers, the TSB construction algorithm makes a broad expansion in the neural nodes thereby forming a clear structure that can be theoretically analysed. While preserving a high accuracy and generalization ability, the TSB expression is clear, differentiable and therefore applicable to dynamic security constrained problems. Furthermore, a transfer learning strategy (TLS) is employed to build TSBs from a limited number of samples in a time-saving way. The possibilities of the developed method are tested via case study that uses the IEEE 39-bus test system. The case study confirmed that the introduced algorithm is highly precise and insensitive to the number of available samples/parameters. This indicates that the proposed method is effective, robust and that as such it may serve as a valuable tool of online TSA.

Among a wide variety of topics that are covered by Dynamic Security Assessment (DSA), maintaining synchronous operation and acceptable voltage profiles stand out. These two stability categories are mostly jeopardized in the seconds after a large contingency occurs. Therefore, this thesis tackles the two aspects of large disturbance stability of power systems in the short-term time scale.

The classical DSA methods deal with the short-term loss of synchronism by analyzing one operating point and one contingency at a time. However, a small change in operating point may turn a stable system unstable. The first part of the thesis overcomes this gap by proposing the idea of parametrizing the stability boundary. The newly introduced method constructs the parametrized security boundaries in polynomial forms based on a reduced amount of Time Domain Simulation (TDS) data. Such a method retains the positive traits of TDS while being able to estimate a measure of stability even for those points that do not belong to the “training" set. The polynomial coefficients are further improved via SIME parametrization that has a physical meaning. Finally, when being subject to a constraint by the means of Quadratic Programming (QP), SIME parametrization also becomes competitive with direct methods in the sense of conservativeness.

Nevertheless, if TDS fails, any TDS-based DSA approach is useless. Most often, the dynamics of the non-linear power system is described by the set of Differential Algebraic Equations (DAE). TDS can face problems when the DAE model experiences singularity due to the loss of voltage causality. This thesis introduces Voltage Impasse Region (VIR) as the state-space area where the voltage causality is lost due to the non-linear modeling of static loads. The entrance of a dynamic trajectory to a VIR was shown to be accompanied by non-convergence issues in TDS and significant voltage drops. Appropriate Voltage Collapse Indicators (VCIs) are also derived for each load model of interest. The thesis concluded that VIR is a structural problem of the DAE model that should always be accounted for when the short-term stability is assessed.

This paper presents a fundamental study of voltage collapses that occur on a post-fault trajectory of a stressed power system in seconds after large disturbances. The focus of the study are voltage collapses that are induced by certain load models. Using an n-machine-N-bus power system model, the paper explicitly shows that the voltage collapse is caused by the non-existence of a real, positive solution for a load voltage magnitude in different areas of a relative rotor angle space when the load is of non-linear type. These "areas without voltage solution" are denoted as Voltage Impasse Regions (VIR) and are mathematically characterized as trigonometric functions of (n-1) relative rotor angles. Once the post-fault trajectory enters a VIR, voltage magnitude solutions become complex or negative, the algebraic Jacobian becomes singular, and the behaviour of a system becomes undefined. The case study has been carried out using a simple 3-machine-1-load system with static load models. In the study, VIR appeared and enlarged as the non-linear (constant power and constant current) load increased. Furthermore, the non-convergence of time-domain solution occurred exactly at VIR, thereby confirming that the problem is of structural nature.

In this paper, an efficient methodology to assess Rotor Angle Stability (RAS) in parameter-space has been proposed. This methodology maps deformations of the power system RAS region under operational changes to a security region in parameter-space that can be assessed on-line. In order to choose the proper parametrization, security boundaries have been constructed using polynomial regression models with coefficients obtained from Ordinary Least Squares (OLS). The identification of suitable parametrization has been carried out, and the newly introduced sensitivity of a SIngle Machine Equivalent (SIME) has been employed to describe the behaviour of a power system along different parameter-space directions. For the chosen parametrization, Constrained Least Squares (CLS) optimization set up as a Quadratic Programming (QP) problem has been used in order to keep the estimates inside the security region. The case study has been carried out using small test systems in two and three-dimensional parameter-spaces.

In this paper, we introduce a wider perspective in Rotor Angle Stability (RAS) analysis, by mapping parts of state-space boundary of interest to parameter space boundary points. These points are obtained using the Time Domain Simulation (TDS), the Closest Unstable Equilibrium Point (UEP) approximation, and the Potential Energy Boundary Surface (PEBS) concepts. Then analytical parameter-space boundaries are constructed using polynomial regression model with optimal fit coefficients in least squares terms. Security boundaries constructed in this manner directly give information about critical clearing times for different faults and operating states, and are suitable as an on-line tool for transient stability assessment.