Fast dynamics of Inverter-Based Generators (IBGs) on the study of transient stability of power systems lead to violations of assumptions commonly employed to justify traditional phasorial RMS models. Short-Time-Fourier Transform (STFT) has been applied in the literature to overcome this issue by representing nonstationary signals in terms of its harmonics as dynamic phasors, maintaining the notion of angles and magnitudes similarly to the traditional phasorial models. Nevertheless, the STFT framework used to represent amplitude and frequency varying sinusoids does not accurately model transient phenomena in power systems due to inherent approximations it entails. Further, STFT dynamic phasors do not have a clear counterpart to complex power, hindering stability studies where customary power formulas are used. This paper presents a novel dynamic phasors theoretical framework able to model nonstationary signals without approximations and offers a theory of nonstationary power. An inverter system attached to an infinite bus is modelled using the proposed framework, yielding a phasorial differential system and simulated under fault, and the time signals reconstructed from the results.

Representation of nonstationary sinusoidal signals as complex time-varying functions, known as Dynamic Phasors (DPs), has been a long-standing problem in the circuit theory and power system stability literatures. The desired features of a theoretical framework for DPs are heavily inspired on classical phasor theory: the ability to transform time differential equations into equivalent algebraic complex equations, while maintaining the familiar notions of phasors, magnitudes and phases, and describing instantaneous power by two components, active and reactive power. Current frameworks rely on integral transforms which need approximations and truncations to allow for practical computation and application and do not offer a theory of nonstationary power. Further, the integral transforms are difficult to operate with and are not suitable to transform any generic nonstationary signal due to convergence requirements and frequency resolution challenges. This paper presents a new theoretical framework for DPs, based on differential operators, that offers a natural and efficient framework to transform nonstationary sinusoidal signals into Dynamic Phasors, while also offering a solid theory on nonstationary power extending the conventional well defined active and reactive power definitions.

With the recent developments of generalized energy functions, it is feasible to extend the existing energy-function-based tools to more general power system dynamical models. In this paper, generalized energy functions are derived for a class of dynamical systems that include, as particular cases, several practical general power system models. As examples, generalized energy functions are derived for lossy network-preserving power system models with both classical synchronous generator and distributed power converters. With the development of these functions, the extension of direct methods for this larger class of power system models becomes feasible.

Load identification is an important issue in power system representations to ensure that simulations will reproduce the dynamic response of a system during a disturbance. For a load model to be accurate, its parameter must be appropriately estimated by a parameter fitness algorithm. The success of the estimation depends mainly on the availability of a good initial parameter guess. If it is not available, the estimation process takes plenty of time to converge or to diverge. This paper proposes a hybrid algorithm based on trajectory sensitivity and generic algorithm. The advantages of the fitness algorithms of Trajectory Sensitivity and Generic Algorithm are combined so as to provide a robust algorithm regarding the initial parameter guess that guarantees the convergence even in the case of unavailability of a good initial parameter set. The combined algorithm was tested in one hundred simulations, in which the initial parameter guesses were randomly generated between limits (parameter uncertainties) for the assessment of the robustness of the algorithm. The results show that in 99 cases, the proposed methodology converged to the true values in a short time.

A new method to group the most effective preventive controls for a set of critical contingencies and select the promising groups considering cost and effectiveness is proposed. This methodology is based on a sensitivity analysis of the maximum loadability point with respect to voltage controls and on a hierarchical clustering analysis. Considering not only the effectiveness of the control elements but also their availability, the methodology design a set of controllers to eliminate all critical contingencies. The methodology was successfully tested in a reduced south-southeast Brazilian system composed of 107 buses.

This paper discusses the foundations and proposes a general framework to decompose the stability analysis of electrical power systems in time-scales. Assuming that the electrical power system model possesses two-time-scale features, the stability analysis of the original two-time-scale power system model is decomposed into the stability analysis of two simpler models: the fast and slow subsystems. Conditions to guarantee that stability of these simpler subsystems implies stability of the complete model are given. The general framework is suitable for stability analysis of power systems in a time frame that can range from a few seconds, which is typically the scenario of transient stability analysis, to a few minutes, which is typical of mid-term stability analysis, in which voltage stability problems are commonly encountered.

The controlling unstable equilibrium point (CUEP) method is a reliable direct method for stability analysis of electrical power systems. In this paper, the foundations of the CUEP method, initially developed for network-reduced power system models, are extended to network-preserving power system models, which are represented by a set of differential-algebraic equations (DAEs). This extension explores the relationship between equilibrium points on the stability boundary of DAE systems and those of their associated singularly perturbed systems (SPS).

This paper proposes a method to assess the practical stability of distribution systems with synchronous generators subject to changes in the system equilibrium conditions due to load variations. The concept of practical stability deals with two known state-space regions Ω1(which contains all the initial conditions reflecting the perturbations at which the system is subject during its operation) and Ω2(which represents the operating security region of the power distribution system) satisfying Ω1⊂ Ω2. The practical stability problem and the focus of this paper is to determine the minimum amount of time in which the system is required to stay in a particular loading condition, such that the system trajectories from an initial condition in Ω1will be confined in the security region of operation Ω2for the whole time interval of interest. This study was carried out using a mathematical model of the distribution system with synchronous generators in the form of a switched affine system. Sufficient conditions for the power distribution system with synchronous generators described as a switched affine system to be practically stable with respect to Ω1and Ω2are given in the form of matrix inequalities constraints. Numerical results were obtained for a model of a cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses.

A new methodology for grouping and selecting the most effective controls for a group of critical contingencies to prevent voltage instability in electrical power systems is developed in this paper. This methodology is based on a sensitivity analysis of the maximum loadability point with respect to voltage controls and on a hierarchical clustering analysis. Considering not only the effectiveness of the control elements but also their availability, the methodology design a set of controllers to eliminate all critical contingencies. The methodology is fast and suitable for on-line assessment of preventive control. The methodology was successfully tested in a reduced south-southeast Brazilian system composed of 107 buses.

In this paper, a new fast method for identification of islanding in power system grids is proposed. This method identifies all the possible cases of island formation, due to the loss of a single equipment (criteria N-1), by means of a single factorization of the bus-branch incidence matrix. The main features of this new method include: (i) simple implementation, (ii) high speed, (iii) absolute identification of all islanding cases of the power system under analysis and (iv) simple identification of buses that compose each island in case of island formation. The method was successfully tested on large-scale systems such as the south-southeast Brazilian system, with 810 buses / 1340 branches.

The behavior of stability regions of nonlinear dynamical systems subjected to parameter variation is studied in this paper. Sufficient conditions to guarantee the persistence of the stability boundary characterization under parameter variation are presented. When these conditions are violated, the stability region may undergo a bifurcation and may suffer drastic changes. In this paper, the behavior of stability region and stability boundary when the system undergoes a type-zero saddle-node bifurcation on the stability boundary is investigated. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation point on the stability boundary is developed. These results are applied to the analysis of stability region of a simple Hopfield artificial neural network.