N.G. Bretas

Main chain representation for evolutionary algorithms applied to distribution system reconfiguration

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.

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.

Node-Depth Encoding and Multiobjective Evolutionary Algorithm Applied to Large-Scale Distribution System Reconfiguration

The power loss reduction in distribution systems (DSs) is a nonlinear and multiobjective problem. Service restoration in DSs is even computationally hard since it additionally requires a solution in real-time. Both DS problems are computationally complex. For large-scale networks, the usual problem formulation has thousands of constraint equations. The node-depth encoding (NDE) enables a modeling of DSs problems that eliminates several constraint equations from the usual formulation, making the problem solution simpler. On the other hand, a multiobjective evolutionary algorithm (EA) based on subpopulation tables adequately models several objectives and constraints, enabling a better exploration of the search space. The combination of the multiobjective EA with NDE (MEAN) results in the proposed approach for solving DSs problems for large-scale networks. Simulation results have shown the MEAN is able to find adequate restoration plans for a real DS with 3860 buses and 632 switches in a running time of 0.68 s. Moreover, the MEAN has shown a sublinear running time in function of the system size. Tests with networks ranging from 632 to 5166 switches indicate that the MEAN can find network configurations corresponding to a power loss reduction of 27.64% for very large networks requiring relatively low running time.

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.

An improved methodology for the design of power system damping controllers

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 fulfil 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.

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.

Fuzzy Stabilization of Power Systems in a Co-Generation Scheme Subject to Random Abrupt Variations of Operating Conditions

In this brief, a new stabilizing controller for the power system of an industrial plant operating in a co-generation scheme is proposed. The main source of perturbations considered in the operating conditions are random abrupt fluctuations in the local load, corresponding to the industrial processes being turned on and/or off. These fluctuations are described as Markovian jumps in the parameters of the power system. The proposed controller follows a standard structure which combines an automatic voltage regulator with a supplementary stabilizing term. This term is obtained with a fuzzy-model-based control technique formulated in the context of linear matrix inequalities under damping and control input constraints. Simulations performed on both a single-machine infinite-bus model and on a multimachine model show the effectiveness of the proposed fuzzy control strategy in reducing the oscillations as well as in maintaining a desired operating condition

Offline Detection, Identification, and Correction of Branch Parameter Errors Based on Several Measurement Snapshots

This paper proposes a three-stage offline approach to detect, identify, and correct series and shunt branch parameter errors. In Stage 1 the branches suspected of having parameter errors are identified through an Identification Index (II). The II of a branch is the ratio between the number of measurements adjacent to that branch, whose normalized residuals are higher than a specified threshold value, and the total number of measurements adjacent to that branch. Using several measurement snapshots, in Stage 2 the suspicious parameters are estimated, in a simultaneous multiple-state-and-parameter estimation, via an augmented state and parameter estimator which increases the V-θ state vector for the inclusion of suspicious parameters. Stage 3 enables the validation of the estimation obtained in Stage 2, and is performed via a conventional weighted least squares estimator. Several simulation results (with IEEE bus systems) have demonstrated the reliability of the proposed approach to deal with single and multiple parameter errors in adjacent and non-adjacent branches, as well as in parallel transmission lines with series compensation. Finally the proposed approach is confirmed on tests performed on the Hydro-Québec TransÉnergie network.