Search

A systematic mixed procedure based on classical and robust control techniques is proposed in this work for the design of robust low-order damping controllers. The procedure formally guarantees a robust performance index for the system in closed-loop by employing a minimum performance index associated with a robust control technique. The mixed approach aims at providing an acceptable and easy-to-use robust design procedure as well as controllers with a simple and typical structure. Besides, a great variety of mathematical tools for the analyses and design of control systems may be employed in the overall procedure. The tests and results have shown that the overall procedure is suitable for the oscillation problem in power systems and that the resulting controllers are robust and effective in the damping of low-frequency electromechanical oscillations. Index Terms--Electromechanical oscillation, linear matrix inequalities, power system stability, power system stabilizers.

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure. Index Terms--Attracting sets, linear matrix inequality (LMI), Lurie problem, Lyapunov methods, nonlinear systems.

This paper presents a set of significant improvements made over a previously developed methodology for the design of controllers to damp electromechanical oscillations in power systems. This previous methodology was able to fulfill several practical requirements of the oscillation damping problem, related to robustness, decentralization, and output feedback structure. However, problems related to an adequate controller gain (to avoid interactions with unmodeled dynamics) and disturbance rejection (allowing the use of noisy input signals, such as the rotor speed measurements) were not treated in this previously reported methodology, and are now addressed in this work. Moreover, the requirement of zero gain in steady-state conditions is now met in a more efficient way. The results of the nonlinear simulations show the satisfactory performance of the designed controllers with respect to the mentioned practical requirements. Index Terms--Damping controllers, electromechanical oscillations, linear matrix inequalities, power system stabilizers.

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. Index Terms--Direct methods, energy function, equilibrium points, load flow, voltage collapse.

Distribution system problems, such as planning, loss minimization, and energy restoration, usually involve network reconfiguration procedures. The determination of an optimal network configuration is, in general, a combinatorial optimization problem. Several Evolutionary Algorithms (EAs) have been proposed to deal with this complex problem. Encouraging results have been achieved by using such approaches. However, the running time may be very high or even prohibitive in applications of EAs to large-scale networks. This limitation may be critical for problems requiring online solutions. The performance obtained by EAs for network reconfiguration is drastically affected by the adopted computational tree representation. Inadequate representations may drastically reduce the algorithm performance. Thus, the employed representation for chromosome encoding and the corresponding operators are very important for the performance achieved. An efficient data structure for tree representation may significantly increase the performance of evolutionary-based approaches for network reconfiguration problems. The present paper proposes a tree encoding and two genetic operators to improve the EA performance for network reconfiguration problems. The corresponding EA approach was applied to reconfigure large-scale systems. The performance achieved suggests that the proposed methodology can provide an efficient alternative for reconfiguration problems. Index Terms--Distribution systems reconfiguration, evolutionary algorithms, main chain representation.

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. Index Terms--Lyapunov methods, nonlinear systems, power systems, stability.

This paper presents a new topological methodology for critical measurements identification in observable networks. A measurement is said to be critical, in an observability sense, if its removal from the measurement set makes the associated system lose observability. The proposed methodology is based on the properties of both, observable measurement subnetworks (OMS) and redundant branch sets (RBS), for the first time proposed. To reduce the combinatorial bluster, the proposed method divides the measurements into two groups and classifies them into two phases. It allows identifying the critical measurements without any numerical calculation. Indeed, it is simple and fast. To clarify the proposed method and to demonstrate its simplicity, two examples are provided. The proposed method is successfully tested in the IEEE-14 bus system as well as in two realistic systems of Brazilian utilities. The first is a 121-bus system by ELETROSUL, and the other is a 383-bus system by Companhia Hidroelectrica do Sao Francisco (CHESF). Index Terms--Critical measurements, graph theory, network observability, state estimation.

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. Index Terms--Damping controllers, electromechanical oscillations, linear matrix inequalities, power system stabilizers.

In many engineering and physical problems, it is very difficult to find a Lyapunov Function satisfying the classical version of the LaSalle's 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. Index Terms--Direct methods, energetic methods, invariance principle, Lyapunov function, transient stability.

The main concern of this paper is the application of the Meinikov 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. Index Terms--Damping estimation, energy methods, transient stability analysis.

In many engineering and physics problems it is very hard to find a Liapunov function satisfying the classical version of the LaSalle's invariance principle. In this work, an extension of the invariance principle, which includes cases where the derivative of the Liapunov 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. Index Terms--Attractor, dissipativeness, invariance principle, stability of manifold of solutions, synchronization, ultimate boundedness.