Luís F. C. Alberto

A new methodology for the coordinated design of robust decentralized power system damping controllers

This paper presents the fundamentals and the algorithm of a new methodology for the design of robust power system damping controllers. The methodology provides controllers capable of fulfilling various practical requirements of the oscillations damping problem, which could not be simultaneously satisfied by the majority of the proposed robust approaches until now. The design procedure is based on a special formulation of the dynamic output feedback control problem, which is very well suited for damping controller design. With this formulation, the design problem (which is originally stated as a set of bilinear matrix inequalities) can be expressed directly in the form of linear matrix inequalities. Furthermore, the formulation allows the incorporation of decentralization constraints on the controller matrices, which are one of the practical requirements for power system damping controllers. Another practical requirement is satisfied with the use of the polytopic model (to ensure the robustness of the closed-loop system with respect to the variation of operating conditions). Moreover, the inclusion of a regional pole placement criterion, as the design objective, allows the specification of a minimum damping factor for all modes of the controlled system. The results show the controller is able to provide adequate damping for the oscillation modes of interest.

On the invariance principle: generalizations and applications to synchronization

In many engineering and physics problems it is very hard to find a Lyapunov function satisfying the classical version of the LaSalles invariance principle. In this work, an extension of the invariance principle, which includes cases where the derivative of the Lyapunov function along the solutions is positive on a bounded set, is given. As a consequence, a larger class of problems may now be considered. The results are used to obtain estimates of attractors which are independent of coupling parameters. They are also applied to study the synchronization of coupled systems, such as coupled power systems and coupled Lorenz systems. Estimates on the coupling term are obtained in order to accomplish the synchronization.

Lyapunov function for power systems with transfer conductances: extension of the Invariance principle

In many engineering and physical problems, it is very difficult to find a Lyapunov Function satisfying the classical version of the LaSalles invariance principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the invariance principle is used to support the proposal of a new function which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.

Application of Melnikov's method for computing heteroclinic orbits in a classical SMIB power system model

The main concern of this paper is the application of the Melnikov method for computing heteroclinic orbits in a classical SMIB power system model and testing the one-parameter transversality condition required in the BCU method for transient stability analysis. First, the Melnikov method is used to give a first approximation for the minimum damping coefficient or, alternatively, for the maximum input mechanical power that should be associated with the system so that the transversality condition is satisfied. This first approximation is obtained without solving any differential equations. After that, this approximation is used as an initial condition for a monotonically convergent process which is very easy to implement and does not require knowledge of fault trajectory at all.

Power system low-voltage solutions using an auxiliary gradient system for voltage collapse purposes

This paper proposes the use of an auxiliary gradient system to calculate the low-voltage solutions (LVSs) of the load flow equations of an electrical power system. It shows that the equilibrium points of that associated auxiliary dynamical system are the solutions of the load flow equations. In such a manner, the paper proposes to find the LVSs by calculating the equilibrium points of the auxiliary dynamical gradient system. The proposed method improves the classical state-space search methods by calculating a new LVS every time the tracked one bifurcates and vanishes. It was tested on Stagg 5-bus, IEEE 39-bus, and IEEE 118-bus systems. The results are at the end of the paper and show that the proposed method presents a great tendency to find the critical LVS for the current load increase direction, as the load is slowly increased.

Direct methods for transient stability analysis in power systems: state of art and future perspectives

This paper presents an overview about the main advances which occurred in the application of a direct method for transient stability analysis. The text is mainly focused on the potential energy boundary surface (PEBS) and boundary controlling unstable (BCU) method. The authors opinion about future perspectives and research areas of interest are given at the end of the text.

Synchronism versus stability in power systems

Abstract In this article, the differences between synchronism and stability and the misuse of these terms in power systems are discussed through examples. It is shown that the swing equations do not present equilibrium solutions if damping coefficients are neglected in the simplified classical model and as a consequence, it is not possible to characterise the stability of the system in the Lyapunov’s sense. Those facts are made clear using power mismatch concepts. Stability studies using One Machine as Reference (OMR) and the Centre of Angle as Reference (COA) are in fact equivalent and do not eliminate the aforementioned problems. A possible solution for these difficulties is developed, that is, modelling the system loads as frequency dependent. A structure-preserving model with the loads as frequency dependent is presented. In the presence of these loads the system can reach equilibrium solutions in velocities other than the synchronous frequency. The equilibrium frequency is calculated through the solution of a structure preserving power flow added to the equation of equilibrium frequency.

Theoretical foundation of CUEP method for two-time scale power system models

This paper presents the foundations of controlling unstable equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale CUEP method is developed. The two-time scale CUEP method is faster and more robust as compared to the traditional CUEP method. Furthermore, more insight into power system dynamics and less conservative estimates of the stability region and critical clearing time are obtained.

Geometrical approaches for gross errors analysis in power systems state estimation

In this paper, a geometrical based approach is used to define the undetectability index (UI) that gives the distance of a measurement from the range of the jacobian matrix. The higher the value of this index the closer this measurement will be to the range of that matrix; the error in measurements with high UI is not reflected in their residues. A critical measurement has infinite UI, belongs to the range of the Jacobian matrix, and its error is totally masked. Using the UI, it is shown measurements not classified as leverage points, and having large masked gross errors in the state estimation process. As example to illustrate the way that UI index works, a two bus power system will be used; to test the index efficiency in identifying the measurements that have the gross errors masked by the state estimation process the IEEE-14 bus system will be used.

Smooth perturbation on a classical energy function for lossy power system stability analysis

The efforts to find Lyapunov functions for power systems with losses have been until now in vain. Despite that, engineers have been using approximated energy-like functions to obtain good estimates of the critical clearing time (CCT) in transient stability analysis of power systems. These approximated energy-like functions are not Lyapunov functions, and are usually obtained by an integration process followed by an approximation of the integration path. Therefore, the good CCT estimates obtained with these functions are not supported by a sound theory. Nevertheless, it is shown in this paper, for a particular approximated energy-like function, a theoretical approach to support these good estimates. The approximated energy-like function studied in this paper is well known in the literature, and was proposed by Athay et al. in the COA formulation. It is shown that this approximated energy-like function is neither a Lyapunov function in the usual sense, nor an extended Lyapunov function, when the transfer conductances are taken into account. In spite of that, a function attending the requirements of the extension of the Invariance Principle, that is, an extended Lyapunov function, can be obtained by smooth perturbations on that energy-like function. This perturbed function can be used to estimate the attraction area without approximations or conjectures. Indeed, the difference between the proposed extended Lyapunov function and the approximated energy-like function has the order of a smooth perturbation. This fact supports the good CCT estimates that have been obtained using these approximated energy-like functions, and encourages engineers to keep using them for CCT estimates.