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This paper is focused on the transient stability constrained optimal power flow (TSC-OPF) problem and its application for determining the optimal dispatch of active and reactive powers of distributed synchronous generators. In order to deal with uncertainties related to the actual active and reactive load values and the network topology configuration, this paper proposes a TSC- OPF formulation that incorporates a set of mathematical constraints based on the trajectory sensitivity analysis (TSA) that represents the impact of different load scenarios and network topologies on the transient stability of the system. The TSC-OPF is solved by an iterative algorithm based on the primal-dual interior point method and the concept of rotor angle first swing (FS) stability. The proposed TSC-OPF is applied for a distribution network constituted by nine buses and two distributed synchronous generators.

When it comes to estimating dynamics (modes) of interconnected power systems through transient (ringdown) data, one can expect more realistic estimates for the compound system if multiple signals distributed over different locations can be used simultaneously during modal estimation. In this context, the contributions of this paper are twofold. First, it is proposed a multi-signal ringdown time-domain Vector Fitting method (‘multi-signal RTD-VF’) which is capable of modeling multiple ringdown signals simultaneously. This method appropriately generalizes the ‘single-signal RTD-VF’ method, which processes ringdown signals independently, i.e., one at a time. Second, it is proposed an instrumental variable (IV) extension of multi-signal RTD-VF. By guaranteeing local optimums after algorithm convergence, such a ‘multi-signal IV-RTD-VF’ formulation may be used for further refining estimates provided by regular multi-signal RTD-VF. Two numerical examples are used to validate the proposed methods. The first example considers actual ringdown data sets extracted from North American Eastern Interconnection (NAEI) and Brazilian Interconnected Power (BIP) systems, whereas the second one considers mode identification of a synthetic signal corrupted by colored noise.

The reduction in bus voltage magnitudes as the load demand grows may lead to sudden disconnection of loads and/or distributed generation units, in distribution grids, caused by undervoltage protection schemes. As proposed in this paper, this discontinuous behavior of distribution grids can be modeled as a sudden load variation in traditional static voltage stability assessment methods, such as the continuation power flow (CPFLOW). A discussion on the impacts of these discontinuities on the equilibrium diagram of the system is presented in this paper, as well as a set of numerical simulations showing that the traditional CPFLOW algorithm presents convergence problems caused by the discontinuities under analysis. From this perspective, this paper proposes an algorithm based on novel predictor/corrector and identification schemes, which are capable of successively calculating the discontinuities that exist in the equilibrium loci of the system under analysis, as well as the maximum loadability point and the type of bifurcation. A simplified modeling approach that eliminates the need for a complex (and computationally expensive), detailed description of distribution grids is also elaborated and incorporated into the proposed algorithm. The simulated examples show that the proposed algorithm adequately handles the problem, yelding more accurate results than the traditional CPFLOW algorithm.

Due to the growing importance of wind farms in the electric power generation matrix in many countries, for example, in Brazil, this paper proposes voltage preventive control actions as an activity to support the programming of the operation of the electric system, based on the ranking of wind power units that most significantly impact the system’s loading margin through the control of its power factor. A sensitivity index is proposed to obtain this ranking, whose mathematical formulation is based on a linear approximation of the power balance equations in the vicinity of the maximum loading point. The system used to test this proposal is a 56-bus system prepared with current real data from the Northeast subsystem of the National Interconnected System of Brazil that includes 22 wind farms with 234 wind turbines, which comprise a total of 600 MW of installed capacity. The results obtained for the 56-bus test system show the applicability of the proposed voltage preventive control actions by indicating the wind farms that can contribute most significantly to the increase in the system’s loading margin from an adequate adjustment of the power factor of these units.

Este trabalho trata sobre a sintonização robusta de Estabilizadores de Sistemas de Potência (ESP) na presença de sinais remotos em um sistema de potência multimáquinas. Os sinais remotos são utilizados para amortecer modos de oscilação do tipo interárea e o tempo de latência é modelado através da aproximação de Padé. A função objetivo considerada para sintonia dos parâmetros dos ESPs almeja maximizar o amortecimento do sistema elétrico de potência para todos os modos de oscilação eletromecânicos e minimizar o impacto das incertezas no tempo de latência, intríseco aos sinais remotos, empregando a técnica da matriz de soma bialternada. A metodologia proposta foi aplicada a um sistema teste composto por 7 barras e 5 geradores considerando vários pontos de operação. A metodologia apresentada garantiu um amortecimento mínimo para todos os pontos de operação e assegurou a estabilidade absoluta do sistema teste para situações onde o tempo de latência é considerado um parâmetro incerto.

In Electrical Power Systems (EPS), traditional voltage stability assessment techniques are based on the solution of algebraic equations to identify the static voltage stability margin (VSM) and the maximum loadability point (MLP) of the system. The estimation of the VSM and the MLP depends on the load growth direction and also on possible events that may occur as the load increases. The main contribution of this paper is to highlight that the actions of undervoltage load shedding (ULS) schemes are important for correct VSM and MLP estimation, which is made through a detailed explanation of the dependence of the MLP on the ULS schemes under contingencies. The paper also shows scenarios where the MLP is reached before any ULS scheme is triggered. The shape of the PV curves in these scenarios where no ULS scheme is activated is shown for a reduced order model of the South-Southeastern part of the Brazilian Interconnected Power System.

Due to the growing demand for energy in the last decades, the electric power system has been facing challenges to supply the power consumed by population. In this sense, isolated microgrids have emerged as a viable alternative based on the use of local energy resources to feed hard to reach areas. In this context, this paper develops a day-ahead energy based on optimal power flow for an isolated microgrid in Brazil equipped with storage system, backup generation and renewable resources. The renewable resource available in the studied microgrid is the photovoltaic solar energy, which presents an intermittent behavior, and so it is modeled by a probability density function in the proposed OPF formulation. The storage system represents approximately 52% of the total microgrid investment. Considering that, the objective function of the OPF incorporates the costs associated to the life cycle of the storage system and the fuel consumption with the backup generation, as well as, a stochastic model to estimate the costs of the photovoltaic solar energy. The proposed formulation was solved using Differential Evolution algorithm to obtain a minimal generation cost considering the load profile of a typical day.

This paper introduces the setup of a Distributed Generation Microgrid (DGM) focused onto research on monitoring (electrical and environmental), controling and operating microgrids. This network is located at the Polytech Center Campus of the Federal University of Parana (UFPR), in Curitiba, Brazil. It consists of nine 13.8 kV feeders, three Distributed Generation (DG) sources and is connected to the main utility through a 69 kV distribution substation of the state electricity company named as Copel DIS. In addition to the electrical configuration, all components of the microgrid are presented, such as power generation, electrical and environmental meters, $\mu \mathrm{PMU}$ and the system monitoring computing environment.

Estimating electromechanical oscillations of power systems plays a crucial role to infer about their stability. In this paper it is proposed a new method in which dominant dynamics of power systems are inferred by analyzing pole estimates produced by several regularized robust recursive least squares (R3LS) implementations operating individually — each one with a different set of autoregressive moving average exogenous (ARMAX) model orders. The proposed method is named “Clustered R3LS”, since it properly adapts the so-called K-means clustering algorithm to automatically model regions of pole agglomeration produced by these individual R3LS implementations. An additional strategy for ignoring (discarding) poles identified as spurious is also part of the proposed Clustered R3LS algorithm. From a practical point of view, Clustered R3LS is here shown to more effectively track dominant dynamics of power systems when compared to Classical R3LS, which is based on analyzing only pole estimates produced by a single R3LS implementation operating with a fixed set of ARMAX model orders that is usually hard to tune. Three case studies are here used to validate the proposed Clustered R3LS method for both ambient and ringdown data. The first and second case studies are based on two well known benchmark models proposed for the analysis of oscillatory dynamics in power systems, whereas the third case study considers actual power system data extracted during a large-scale event from the Brazilian Interconnected Power (BIP) system.

The synchrophasor data provided by wide-area measurement systems have potential applications in electric power systems such as the use of these measurements as control inputs of wide-area damping controllers (WADCs) for small-signal stability enhancement. However, synchrophasor data are particularly vulnerable to cyber attacks (such as denial-of-service attacks) that can cause communication link failures in a smart grid communication network and, consequently, compromise the power system stability. In order to reduce the impact of communication failures on the performance of a WADC, this paper proposes a method to design a WADC considering robustness to multiple operating points, time delays in the communication channels and possible permanent loss of communication signals in the input and the output of the controller (which may be due, e.g., to denial-of-service cyber attacks). The performance of the designed controller is evaluated using modal analysis and nonlinear time-domain simulations in one of the IEEE benchmark systems to validate the results: the Simplified 14-Generator Model of the Southeastern Australian Power System.

This paper proposes a novel method, called Ringdown Time-Domain Vector Fitting (RTD-VF), for estimating electromechanical modes in interconnected power systems. Such a method authentically extends, to the context of ringdown analysis, the well known Time-Domain Vector Fitting (TD-VF) method, which has already been successfully applied within other power systems areas. The proposed method is based on a state-space discretization framework which enables ringdown events to be effectively estimated when described as artificial unit impulse responses. Moreover, RTD-VF completely avoids the necessity to perform discrete Fourier transforms (DFTs) of ringdown data sequences. Three case studies are used to validate the proposed method. One of the examples considers a synthetic test signal, whereas the other two case studies consider actual ringdown data sets extracted from the North American Eastern Interconnection (NAEI) system and from the Brazilian Interconnected Power (BIP) system.

The separation of low-frequency electromechanical modes from spurious modes is a challenging problem in ambient data analysis performed by identification and signal processing techniques. In order to accurately extract all relevant dynamic properties from power system ambient measurement data, a filtering pre-processing step and high-order models are usually adopted during the identification process for an effective handling of noise, which may lead to the appearance of the so-called spurious modes into the identified system model. These spurious modes have no physical relevance, but they may present similar characteristics to the low-frequency electromechanical modes, affecting the accurate evaluation of the latter ones. Hence, this paper proposes a post-processing technique based on modal stabilization diagrams to distinguish low-frequency electromechanical modes and spurious modes from ambient data analysis. This proposed post-processing technique is applied in simulated and real measured ambient data with the purpose of estimating the dynamic properties of inter-area modes in large interconnected generation and transmission power systems (IPSs), as well as, global and local modes in active distribution networks (ADNs) with distributed generation (DG) based on synchronous generators.

This paper presents an analytical method based on the solution of the nonlinear Riccati equation for the design of coordinated, decentralized damping controllers for power systems. While other approaches use analytical methods that ensure robustness with respect to uncertainties in the system operating conditions by considering a controller of the same order as the plant, which results in high-order controller structures, the proposed method has the advantage of providing robust and decentralized low-order controllers. The method is applied to two IEEE benchmarks, and the designed controllers are assessed by modal analysis and nonlinear time-domain simulation.

This paper is concerned with the finite-time stability problem of a class of linear continuous-time non-homogeneous switched systems under a time-dependent switching signal constrained by a dwell-time T . Once the finite-time stability is guaranteed, one of the main results of the paper guarantees that any system trajectory starting in a subset Ω 1 of the state-space will remain in Ω 2 ⊃ Ω 1 over a finite time interval and for any switching sequence with a dwell-time T ≥ T . The finite-time stability conditions are provided in the form of bilinear matrix inequalities (BMIs), which can be transformed to linear matrix inequalities (LMIs) by means of a step-by-step procedure that includes the computation of the sets Ω 1 and Ω 2 by the knowledge of the system operating range. Three illustrative examples are used to show the validity of the results.

This paper proposes an algorithm for the application of mode decomposition techniques based on ringdown signals to estimate electromechanical modes in electrical power systems. The estimation of the electromechanical modes is done by defining parameters for the application of modal estimation technique successive times, followed by routines of identification and analysis of the results. Results are obtained by using the techniques LS-ESPRIT, TLS-ESPRIT and WTLS-ESPRIT. The simulations were performed for a distribution network in the presence of a group of three synchronous generators.

This paper presents the results of an ongoing project involving the monitoring of micro phasor measurement units (micro-PMU) at Universidade Federal do Parana (UFPR). The infrastructure for receiving, processing and storing data from micro-PMUs, energy meters and power quality analysers was deployed. Free software were tested for data storage and visualization. We modified an existing open-source Energy Monitoring System (EMS) for proper use with PMUs. The software native communication protocol was adapted from hypertext protocol (HTTP) to direct reception of user datagram protocol (UDP) in IEEE Std. C37.118.2-2011 format to receive micro-PMUs transmission at 120 phasor per second. We modified data storage format to efficiently deal with time information allowing reduction of 60% of storage space in comparison to commonly used phasor data concentrator (openPDC).

The automatic controllers of reactive power (var) and power factor (pf) have appeared in specifications from power plants when distributed generation is applied. Some studies reinforce the use of these types of controllers on distributed synchronous generators (DSGs) can lead to problems related to voltage quality and oscillations’ damping associated with electromechanical modes. It follows, therefore, as a possible alternative to minimize the adverse effects of such oscillatory modes during operative situations involving the use of these controllers, the joint design of var/pf controller and a local supplementary damping controller, also called power system stabilizer (PSS). In this scenario, this paper presents a tuning methodology of PSS and var/pf controller for DSGs, which is based on the optimization of dynamic performance indexes employing eigenstructure allocation. In general, the goal is to increase the damping of the electromechanical oscillatory modes, as well as to minimize the energy of the oscillations from the rotor speed and the field voltage. Both controllers are tuned simultaneously, avoiding adverse interactions among them. The methodology is applied for the design of the control loop of a DSG operating in a distribution network of 33 kV with 6 buses. The evaluation of the controllers’ performance is done through modal analysis and nonlinear simulations for a set of different operating conditions.

The power system dynamic response is impacted by uncertainties in the system operation such as load variation and large penetration of intermittent generation. This paper presents a method based on the solution of the nonlinear Riccati equation for the design of coordinated robust damping controllers for power systems. The resulting robust controller is of practical application (fixed-order) with a performance guarantee based on quadratic stability. The method is applied to the 68-bus 5-area benchmark test system and the designed controllers are assessed by modal analysis and nonlinear time simulation. The obtained results show better performance of the proposed method compared to benchmark controllers.

The idea of a smart grid is based on the increased integration of information technologies throughout the power grid. Technologies, such as phasor measurement units, are being deployed to increase the number of wide-area measurements across the bulk power system providing increased awareness of the system operational state. However, from a critical infrastructure perspective, the advanced metering infrastructure introduces a concern: the loss of communication among devices and the power grid. This communication loss may interfere with the wide-area control system performance and adversely affect the power system dynamics. This paper proposes a method based on genetic algorithms for wide-area robust damping controller design considering multiple operation points and loss of communication links related to the input and to the output of the central controller. The method is applied to enhance the damping of the electromechanical oscillations in an IEEE benchmark system: the simplified 14-generator model of the Southeastern Australian power system. The performance of the designed controller is evaluated using modal analysis and non-linear simulations in the time domain. The obtained results demonstrate the effectiveness of the method to design a single centralized controller that provides satisfactory damping to the electromechanical oscillations over several operating points, even when there is a loss of a communication link, thus being robust with respect to is an important aspect of a critical power grid infrastructure.

This paper proposes the use of a particular class of linear differential inclusion (LDI) for the estimation of regions of attraction of asymptotically stable equilibrium points of nonlinear dynamical systems with time-varying parametric uncertainties bounded by a polytope. In this paper, we provide a systematic procedure based on the mean value theorem in conjunction to a linear matrix inequality based approximation technique to obtain the description of the uncertain nonlinear system via the proposed LDI form, which can be written equivalently as a particular class of a time-varying linear system. Through this suitable system representation in the form of this time-varying linear system, a numerical algorithm based on convex optimization is proposed to determine these regions of stability. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

This paper proposes the design of a linear quadratic regulator (LQR) for a class of nonlinear systems modeled via norm-bounded linear differential inclusions (NLDIs). The system to be controlled is originally described by a nonlinear dynamical model in state-space form. For synthesis purposes, however, this nonlinear system is represented in the form of an NLDI. Using an approach based on the mean-value theorem, this NLDI considers the nonlinear terms in the Taylor series expansion of the nonlinear equations as uncertainties in the model. The main contribution of this paper is the construction of a procedure to design an LQR controller for the NLDI representation of the nonlinear system, in such a way that the properties guaranteed to the NLDI model by the controller will also be valid for the underlying nonlinear system. The control design problem is formulated as an optimization problem in the form of bilinear matrix inequalities (BMIs) and solved via an iterative process known as V-K iterations. A numerical example is presented at the end of this paper to demonstrate the effectiveness of the LQR controller to this class of systems.

Distributed generation (DG) usage is increasing nowadays, specially in the wider sense of microgrids. Its technical impacts and restrictions are still under study, and in several aspects are kept almost untouched. One of these aspects is the small-signal stability of distribution systems in the presence of distributed synchronous generators (DSG). This paper deals with such problem, presenting a comprehensive small-signal stability study of a system under the specified conditions. The study considers two types of excitation control for synchronous generators: voltage and power factor. The focus, however, is on the latter, since it is the most widely used in distributed generators connected to distribution grids. Thus, a comparative analysis between these two control strategies is performed, allowing the investigation of their effects on the small-signal stability of a power distribution system (PDS). This comparative analysis is performed with respect to the characteristics of its electromechanical oscillation modes (EOM) under several DG penetration levels. Copyright © 2010 John Wiley & Sons, Ltd.

The design of supplementary damping controllers to mitigate the effects of electromechanical oscillations in power systems is a highly complex and time-consuming process, which requires a significant amount of knowledge from the part of the designer. In this study, the authors propose an automatic technique that takes the burden of tuning the controller parameters away from the power engineer and places it on the computer. Unlike other approaches that do the same based on robust control theories or evolutionary computing techniques, our proposed procedure uses an optimisation algorithm that works over a formulation of the classical tuning problem in terms of bilinear matrix inequalities. Using this formulation, it is possible to apply linear matrix inequality solvers to find a solution to the tuning problem via an iterative process, with the advantage that these solvers are widely available and have well-known convergence properties. The proposed algorithm is applied to tune the parameters of supplementary controllers for thyristor controlled series capacitors placed in the New England/New York benchmark test system, aiming at the improvement of the damping factor of inter-area modes, under several different operating conditions. The results of the linear analysis are validated by non-linear simulation and demonstrate the effectiveness of the proposed procedure.

Essa pesquisa se propõe a investigar o uso de Inclusões Diferenciais Lineares Limitadas por Norma (IDLNs) para projeto de controladores de amortecimento de tipo PSS (Power System Stabilizer) para sistemas elétricos com a presença de geração distribuída. Uma vez definida de maneira adequada, uma IDLN pode ser capaz de englobar um conjunto de trajetórias do modelo não-linear do sistema em estudo. Assim, é possível garantir certas propriedades (estabilidade assintótica, por exemplo) para as trajetórias da IDLN e, consequentemente, as mesmas propriedades terão validade para as trajetórias do modelo não-linear. Inicialmente propõe-se um procedimento para cálculo dos parâmetros do modelo de IDLN proposto de forma que ela seja capaz de agregar um conjunto de dinâmicas de interesse do sistema. Tal procedimento divide-se, basicamente, em duas etapas. Na primeira etapa, o objetivo é englobar um conjunto de trajetórias do modelo não-linear do sistema numa Inclusão Diferencial Linear Politópica (IDLP). Já na segunda etapa, os parâmetros da IDLN são calculados a partir da solução um problema na forma de LMIs (Linear Matrix Inequalities) que utiliza informações da IDLP obtida anteriormente. Em seguida, essa pesquisa propõe um procedimento sistemático na forma de LMIs para projeto de controladores de amortecimento de tipo PSS para sistemas de geração distribuída usando-se os modelos de IDLNs propostos. Restrições na forma de desigualdades matriciais são incluídas ao problema de controle para garantir um desempenho mínimo a ser atingido pelo controlador. Como resultado, a formulação do problema de controle é descrita por um conjunto de BMIs (Bilinear Matrix Inequalities). Entretanto, através de um procedimento de separação pode-se tratar o problema em duas etapas, ambas envolvendo a solução de um conjunto de LMIs. Uma planta de co-geração instalada numa rede de distribuição composta por um alimentador e 6 barras é utilizada como sistema teste. This work proposes an investigation about the use of Norm-bounded Linear Differential Inclusions (NLDIs) for the design of PSS-type damping controllers for electrical systems with the presence of distributed generation. When the NLDI is properly defined, it is possible to guarantee certain properties (for example, asymptotic stability) to the trajectories of the NLDI and, consequently, the trajectories of the nonlinear model have these same properties. Initially, this research proposes a procedure to calculate the NLDI parameters in such way it can be capable to aggregate a set of dynamics of interest. Such procedure is constituted by two steps. In the first step, the objective is to aggregate some trajectories of the nonlinear model to a Politopic Linear Differential Inclusion (PLDI). In the second step, the NLDI parameters are calculated by solving a problem in the form of LMIs (Linear Matrix Inequalities) that uses the IDLP previously obtained. After that, this research proposes a systematic method based on LMIs for the design of PSS-type damping controllers for distributed generation systems. Such method uses the proposed NLDI models. Constraints in the form of LMIs are included to the control problem formulation in order to guarantee a desirable performance to the controller. As a result, the control problem formulation is structured by a set of BMIs (Bilinear Matrix Inequalities). However, it is possible to deal with such problem in two steps,both involving the solution of a set of LMIs. A cogeneration plant added to a distribution network constituted by a feeder and six buses is adopted as test system.

A common approach to deal with transient stability constraints in optimization problems is the combination of a numerical discretization method with interior point methods (IPMs) for solving large-scale nonlinear programming (NLP). The numerical discretization is adopted to convert the differential equations that describe the electromechanical transients in power systems in a set of algebraic equations to be included into a conventional optimal power flow (OPF) problem. The resulting transient stability constrained optimal power flow (TSC-OPF) problem, however, suffers with the curse of dimensionality, high computational time and memory consumption to solve it, even for small systems. To relieve this computational burden, this paper proposes an algorithm that aims at solving a TSC-OPF problem via primal-dual IPM with only a few time steps of numerical discretization in post-fault period, which is enough to ensure the rotor angle first swing stability. Once the TSC-OPF problem is solved, a numerical discretization method is applied to calculate the system trajectory from the first rotor angle peak in post-fault period. An important contribution of the proposed algorithm is to provide a proper accuracy on the computation of constant admittance loads. Numerical results are obtained for a 9-bus distribution network with the purpose of providing a proper sizing of DG units based on synchronous generators and an optimal operation to the network.

This paper proposes a method to assess the practical stability of power distribution systems with synchronous generators subject to changes in the system equilibrium conditions due to fast varying loads. 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 under which conditions the system trajectories will be confined into a security region of operation for a certain time interval of interest, as the equilibrium point of the model changes. This study was carried out using a mathematical model of the distribution system with synchronous generators in the form of a switched affine system. This proposed model is capable of describing the system behavior over a certain period within which changes on the equilibrium conditions of the system can occur. Sufficient conditions for the power distribution system with synchronous generators described as a switched affine system to be practically stable with respect to its operating security region Ω2 are given in the form of matrix inequalities constraints. The results, obtained for the model of a cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses, show that the less stringent properties of the concept of practical stability can be very well-suited to the security analysis of power systems subjected to frequent variations in the load level.

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 Ω1 will be confined in the security region of operation Ω2 for 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 Ω1 and Ω2 are 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.

This paper presents a new methodology for the design of power oscillation dampers (PODs) for synchronous generators connected to distribution networks. The proposed methodology provides controllers capable of fulfilling robustness requirements and also making an effective trade-off between oscillation damping enhancement and generator terminal voltage performance. A description of the nonlinear dynamical model to be controlled in the form of norm-bounded linear differential inclusions (NLDIs) is adopted at the design stage of the controller. This is different from most of the existing POD design methods, where the control design is essentially based on a simplification of the nonlinear dynamical model in the form of linear time-invariant (LTI) models. The use of NLDIs allows us to consider the system nonlinearities as model uncertainties, and then we take into account such uncertainties at the controller design stage using a robust control methodology. Once that this NLDI takes the nonlinear behaviors of the system into account, it can better represent the relatively large excursions that occur in the system states, allowing us to add a constrain to the control problem formulation imposing a certain acceptable performance to the generator terminal voltage during transients. The proposed algorithm can be easily handled by using linear matrix inequalities (LMIs) solvers. A cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses is adopted as a test system. The results show that the two designed objectives are quite satisfactorily achieved.

In this paper, the problem of practical stability of some classes of continuous-time switched systems is studied. The main results of this paper include some sufficient conditions concerning practical stability of continuous-time switched nonlinear systems without a common equilibria for all subsystems. In this class of switched systems, the equilibrium point varies discontinuously according to a time-dependent switching signal. So, stability with respect to a set, rather than a particular point, is discussed. Using this preliminary result, we present sufficient conditions in the form of linear matrix inequalities (LMIs) for practical stability of a particular class of switched systems without common equilibria: the switched affine systems. An illustrative example is presented to show the validity of the results.

This paper proposes a systematic method based on linear matrix inequalities for the design of power system stabilizers for synchronous generators connected to distribution grids. The system to be controlled is originally described by a nonlinear dynamical model in state-space form. However, for synthesis purposes we represent it as a norm-bounded linear differential inclusion model. Using an approach based on the mean-value theorem, this linear representation considers the nonlinear terms in the Taylor series expansion of the nonlinear equations as uncertainties in the model. Constraints are included to the control problem formulation in order to guarantee a satisfactory performance of the controlled system. The main objectives, from the application viewpoint, are the enhancement in the damping of electromechanical oscillations, as well as the minimization of the peaks reached by the terminal and field voltages during the transients of interest. The proposed algorithm is a straightforward design procedure and can be easily handled by using LMI solvers. A cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses is adopted as test system, and the results show that the two designed objectives are quite satisfactorily achieved.

It is well known that power system stabilizers (PSSs) may cause adverse impacts to the transient performance of generator terminal and field voltages when they are not properly designed. This fact, in special for distribution networks with synchronous generators, is relevant from the voltage quality point of view since the operation of sensitive equipments connected to the network may be deteriorated. Based on these facts, this paper proposes an iterative method to tune PSSs for distributed synchronous generators (DSGs) that performs an effective trade-off between transient voltage performance and oscillation damping enhancement. Our proposed tuning procedure uses an optimization algorithm that works over a formulation of the classical tuning problem in terms of bilinear matrix inequalities (BMIs). Using this formulation, it is possible to apply linear matrix inequality (LMI) solvers to find a solution to the tuning problem via an iterative process, with the advantage that these solvers are widely available and have well-know convergence properties. The system that was analyzed has 1 feeder, 7 buses and a cogeneration plant injecting 10 MW to the network.

In this paper, a new procedure to design Supplementary Damping Controllers (SDCs) for Flexible Alternating Current Transmission System (FACTS) devices is proposed. The control design problem is formulated as a search for a feasible controller subject to restrictions in the form of Linear Matrix Inequalities (LMIs). The main objective, from the application viewpoint, is the improvement of the damping ratios associated to inter-area oscillation modes. Unlike other types of formulations existing in the literature, this new formulation is capable of explicitly modeling the constraints on the controller bandwidth, which are crucial to avoid undesired amplification of high frequency noise signals coming into the controller input. To illustrate the efficiency of the proposed procedure, the design of an SDC for a Thyristor Controlled Series Capacitor (TCSC) placed in the New England/New York benchmark test system is carried out. The results show the designed controllers are able to provide adequate damping for the oscillations modes of interest for several different operating conditions. Este artigo propõe um novo procedimento para projeto de controladores suplementares de amortecimento (ou SDCs, do inglês Supplementary Damping Controllers) para dispositivos FACTS. O problema de projeto do controlador é formulado como uma busca por um controlador que satisfaça um conjunto de restrições na forma de desigualdades matriciais lineares (ou LMIs, do inglês Linear Matrix Inequalities). Sob o ponto de vista de aplicação, o objetivo principal de controle é aumentar as taxas de amortecimento das oscilações inter-área. Ao contrário de outras formulações propostas na literatura, esta nova formulação é capaz de modelar, explicitamente, as restrições da banda passante do controlador, evitando assim que ruídos em alta frequencia sejam amplificados a partir do sinal de entrada do controlador. Para ilustrar a eficiência do procedimento proposto foi realizado um projeto de controlador suplementar para dispositivos TCSC instalados no sistema New England/New York. Os resultados mostram que os controladores projetados são capazes de fornecer amortecimento adequado para os modos de oscilação de interesse em diversas condições de operação.

This paper presents a systematic method for the robust design of a supplementary controller for a TCSC device to damp inter-area oscillations in electric power systems. The method is based on a robust control technique structured in the form of linear matrix inequalities (LMIs). The polytopic model is used to guarantee the robustness of the controller with respect to the variations in the operating points of the system. The minimum damping ratio is used in the design stage as performance index for the closed loop system. The proposed controller is based on dynamic output feedback and uses only a local measurement of the active power flow as input signal for the controller, so communications links are avoided. The "feasp" solver, available in Matlab LMI Control Toolbox, is used to solve the set of LMIs formulated for the control problem. Performance analyses of the closed loop system were carried out by means of modal analysis and nonlinear simulations, showing that the controller is effective in improving the damping of inter-area oscillations of a two-area four-machine test system for several different operating points.

The paradigm that distribution networks are free from problems related to electromechanical oscillations (due to their mainly passive nature and relatively large resistances) is about to change with the increase in the number of small generators connected to them. This paper shows a real situation in which the connection of a few small generators in the distribution network can significantly deteriorate the damping in the system response to small perturbations. The effects of the system response on the power quality across the network are also discussed. The analyzed system is located within the state of Sao Paulo, Brazil, having 3 feeders (comprising 57 kilometers of cables) and 32 buses distributed along these feeders. The need for an adequate assessment of the oscillations and their impacts over power quality is pointed out. It is shown that conventional PSSs can be a simple, cheap, and effective solution to keep the power quality standards as the number of generators entering the grid increases.

This paper presents a simultaneous coordinated design of PSS-type and TCSC supplementary damping controllers for electric power systems. Such controllers are designed by means of a systematic methodology based on robust control. The adopted technique is an extension of a previously presented methodology. The design procedure is structured in the form of linear matrix inequalities (LMIs). The controllers are obtained by means of a numerical solution of the LMIs describing the control problem. Possible undesirable interactions between the PSS-type damping controllers and the TCSC damping controller are avoided by using the multimachine model in the design stage. The proposed technique ensures that the designed controllers fulfill various practical requirements of the oscillation damping problem in power systems. The minimum damping ratio is used as performance index for the system in closed loop. The proposed controllers were simultaneously designed and they have provided a coordinated control action and a satisfactory performance for the power system, as shown in the results.

This paper presents a robust control scheme for a STATic Synchronous COMpensator (STATCOM) coupled with a Battery Energy Storage System (BESS) for improving the dynamic oscillations damping and the transmission power quality in electric power systems. The presented STATCOM/BESS controls both reactive and active power injection/absorption to/from the power system. It is investigated the performance of a Supplementary Damping Controller (SDC) added to the reactive power control scheme. The SDC is designed by a robust control technique structured in the form of linear matrix inequalities (LMIs). The main objectives, from the application viewpoint, are the improvements of the damping of oscillations in tie-lines (precisely, voltage and active power flow oscillations which are related to the presence of inter-area oscillations mode), and also, the minimization of their peak values during transients. The tests were realized in a two-area four-machine power system, and the results show the proposed control scheme presents a good performance for several different operating points.

In the context of static Voltage Stability Assessment (VSA), as the power system load grows, bus voltages tend to drop. This reduction may lead to generator or load disconnections caused by undervoltage protection schemes. These events comprise sudden parametric variations that affect the equilibrium diagram and the Voltage Stability Margin (VSM) of power systems. Practical examples of such sudden load changes are caused by the mandatory disconnection of Distributed Generation (DG) units and Undervoltage Load Shedding (ULS). There are no thorough studies in the literature concerning these load parametric variations and the discontinuities that they cause in power system equilibria. This dissertation describes a predictor/corrector scheme specifically designed to handle these discontinuities, so it is possible to evaluate their effect on the VSM of power systems. This method successively calculates the load discontinuities that exist in the equilibrium locus of the system under analysis. It results in the sequence of sudden load variations that happens and their overall impact on the system. When applied to quantify the effect of DG mandatory disconnections and ULS, the proposed predictor/corrector scheme yielded better results than the traditional Continuation Power Flow (CPFLOW), which experienced convergence problems caused by the discontinuities under analysis. However, due to its design, the applicability of the proposed method should be restricted to power systems that go through several successive sudden load changes. In this sense, it should not be regarded as a replacement for the CPFLOW, but rather as a technique that could award this traditional VSA tool with new features to enhance its performance. No contexto de análise estática de estabilidade de tensão, conforme a carga de um sistema de potência cresce, as tensões nas suas barras tendem a cair. Essa redução pode causar a desconexão de geradores e cargas devido a atuação de proteções de subtensão. Esses eventos representam variações abruptas de demanda que alteram o diagrama de equilíbrio de um sistema e sua Margem de Estabilidade de Tensão (MET). Exemplos práticos dessas variações são causados pelo desligamento mandatório de unidades de Geração Distribuída (GD) e pelo Corte de Carga por Subtensão (CCS). Não há estudos detalhados na literatura que trabalham especificamente com essas variações nos parâmetros da carga, nem com as descontinuidades que elas causam no diagrama de equilíbrio de sistemas de potência. Essa dissertação descreve um procedimento especificamente projetado para lidar com essas descontinuidades, de modo que seja possível avaliar seu efeito na MET de sistemas elétricos. Esse método calcula sucessivamente as descontinuidades de carga que existem no diagrama de equilíbrio do sistema em análise. Ele resulta na sequência de variações súbitas de carga que ocorre e no seu impacto no sistema. Quando o método foi aplicado para quantificar o efeito do desligamento mandatório de GD e do CCS, ele apresentou resultados melhores do que o tradicional Fluxo de Carga Continuado (CPFLOW), o qual sofreu problemas de convergência causados pelas descontinuidades em questão. Entretanto, devido ao seu projeto, o método proposto só deve ser utilizado para sistemas de potência que estão sujeitos a várias sucessivas variações abruptas de carga. Por essa razão, esse método não pode ser considerado um substituto do CPFLOW, mas sim como uma técnica capaz de agregar novas funcionalidades a essa ferramenta tradicional, amentando assim seu horizonte de aplicações.