[pt] Os sistemas elétricos de grande porte estiveram sempre fortemente associados à utilização de máquinas síncronas para a geração de energia e atendimento às cargas, tendo como outros benefícios, a possibilidade de prover o controle dinâmico do perfil de tensão da rede e a regulação da frequência elétrica. Em relação ao controle da frequência, as máquinas síncronas agregam resposta inercial, ou seja, convertem em energia elétrica parte da energia cinética armazenada em seus rotores, e vice-versa, sempre que caracterizado um desequilíbrio entre carga e geração. Este comportamento determina as taxas iniciais de variação da frequência elétrica (RoCoF – Rate of Change of Frequency), as quais podem ser definidas principalmente por dois fatores: a magnitude do desbalanço de potência ativa e a inércia global do sistema, sendo esse último dependente do número de geradores sincronizados e da inércia de cada gerador. O crescimento cada vez maior na matriz de energia elétrica de usinas eólicas e solares fotovoltaicas, que usualmente conectam-se à rede por meio de conversores eletrônicos e, portanto, não agregam resposta inercial ao sistema, trará impactos na regulação da frequência e nos valores de RoCoF. Nesse cenário, o principal objetivo deste trabalho é apresentar uma análise quantitativa da evolução das taxas de variação da frequência no SIN durante perdas de grandes blocos de geração. Os valores de RoCoF são analisados tanto do ponto de vista global, através da frequência no centro de inércia do sistema, quanto do ponto de vista regional, a partir de barras que representam as regiões do SIN. / [en] Large electrical systems have always been strongly associated with the use of synchronous machines for power generation and load service, with other benefits, possibility of providing dynamic control of the system voltage profile and frequency regulation. Regarding frequency control, synchronous machines aggregate inertial response, i.e., convert part of the kinetic energy stored in their rotors into electrical energy (and vice-versa), whenever there is an imbalance between load and generation. This behavior determines the initial Rate of Change of Frequency (RoCoF), determined mainly by two factors: a magnitude of the active power unbalance and the global inertia of the system, that is dependent on the number of synchronized generators and the inertia of each generator. The increase of wind and solar photovoltaic plants in electrical energy matrix, which are usually connected to the system through inverters and do not aggregate inertial response to the system, will impact on frequency regulation and RoCoF values. In this scenario, the main objective of this thesis is to present a quantitative analysis of the evolution of RoCoF in the Brazilian Electrical System during outages of large generation blocks. RoCoF values are analyzed from a global point of view, through the frequency at the center of inertia of the system, and from a local point of view, through buses that represent the Brazilian Electrical Subsystems.

This report addresses the parameter settings for a protective relay designed to safeguard a 15 kW wind turbine located in Rimbo, Norrtälje municipality, against unintentional islanding. This type of situation arises when distributed energy resources continue to supply local loads, even if the main grid has been unintentionally disconnected. The previous protection system experienced malfunctions and has been replaced with a new protective relay to ensure reliable protection. The new protective relay introduces two parameters (relay settings) associated with unintentional islanding protection function, namely RoCoF (rate of change of frequency) hysteresis, and delay, which were not defined in the previous protective relay. This report aims to determine suitable relay settings and verify that the relay operates as intended, taking into account both local and national requirements for connected generators. When these requirements did not specify or recommend a specific value, reference was made to practices in neighbouring countries, and consideration was given to the generator owner's benefit. Testing the relay with the chosen settings was crucial to ensure a correct understanding and accurate input of the settings. The testing was conducted in a laboratory environment with carefully defined signals of controlled frequency and voltage, while the relay's trip output was logged. The report includes information about the current settings along with a theoretical background to explain their functionality. It also presents test results and the provided information on parameter configurations. Additionally, recommended settings for RoCoF hysteresis and implementation delay are suggested, aiming to enhance protection against inadvertent operation. The results confirmed that the relay can be used in Rimbo, Norrtälje municipality, according to the parameters described in the report. / Denna rapport behandlar parameterinställningar för ett skyddsrelä som skyddar en 15 kW vindkraftsturbin i Rimbo, Norrtälje kommun, mot oavsiktlig ödrift. Denna typ av situation uppstår när distribuerade energiresurser försätter att mata lokala laster, även om stamnätet har kopplats bort oavsiktlig. Det tidigare skyddssystemet har blivit skadat och ersatt med ett nytt skyddsrelä för att säkerställa ett tillförlitligt skydd. Det nya skyddsreläet introducerar två parametrar (reläinställningar) relaterade till skyddsfunktionen mot oavsiktlig ödrift, nämligen RoCoF (frekvensderivata intervall) hysteres och fördröjning, som inte var definierade i det tidigare skyddsrelät. Denna rapport syftar till att fastställa lämpliga reläinställningar och verifiera att reläet fungerar enligt avsikt, med hänsyn till både lokala och nationella krav för anslutna generatorer. När dessa krav inte specificerade eller rekommenderade ett specifikt värde, refererades det till praxis i närliggande länder och hänsyn togs till generatorägarens fördel. Testning av reläet med de valda inställningarna var av central betydelse för att säkerställa en korrekt förståelse och korrekt inmatning av inställningarna. Testningen utfördes i en laborationsmiljö med noggrant definierade signaler av kontrollerad frekvens och spänning, samtidigt som reläets utlösningsutgång loggades.  Rapporten inkluderar information om de aktuella inställningarna tillsammans med en teoretisk bakgrund för att förklara deras funktion. Den presenterar också resultat från tester och den tillhandahållna informationen om parameterinställningar. Dessutom rekommenderas inställningar för RoCoF-hysteres och fördröjning för implementering, med målet att förbättra skyddet mot oavsiktlig ödrift. Resultaten konstaterade att reläet kan användas i Rimbo, Norrtälje kommun enligt de parametrar som beskrivs i rapporten.

The thesis deals with the issue of measurement of frequency and its derivative (RoCoF) in simulation software. The aim of the thesis was to compare results obtained in three different pieces of software (PSS/E, PSCAD, MODES). 2 disturbances were simulated in a grid model IEEE 39 bus system and values of frequency and generator speed were assessed. The results obtained in different software are diverse. This is influenced by method of modelling of synchronous generator and algorithm of calculation of frequency. Findings are important for future investigation of power system transients in simulation software and also point to potencial incorrect assassement of frequency in protective relays.

We consider a class of periodic preventive maintenance (PM) optimization problems, for a single piece of equipment that deteriorates with time or use, and can be repaired upon failure, through corrective maintenance (CM). We develop analytical and simulation-based optimization models that seek an optimal periodic PM policy, which minimizes the sum of the expected total cost of PMs and the risk-averse cost of CMs, over a finite planning horizon. In the simulation-based models, we assume that both types of maintenance actions are imperfect, whereas our analytical models consider imperfect PMs with minimal CMs. The effectiveness of maintenance actions is modeled using age reduction factors. For a repairable unit of equipment, its virtual age, and not its calendar age, determines the associated failure rate. Therefore, two sets of parameters, one describing the effectiveness of maintenance actions, and the other that defines the underlying failure rate of a piece of equipment, are critical to our models. Under a given maintenance policy, the two sets of parameters and a virtual-age-based age-reduction model, completely define the failure process of a piece of equipment. In practice, the true failure rate, and exact quality of the maintenance actions, cannot be determined, and are often estimated from the equipment failure history. We use a Bayesian approach to parameter estimation, under which a random-walk-based Gibbs sampler provides posterior estimates for the parameters of interest. Our posterior estimates for a few datasets from the literature, are consistent with published results. Furthermore, our computational results successfully demonstrate that our Gibbs sampler is arguably the obvious choice over a general rejection sampling-based parameter estimation method, for this class of problems. We present a general simulation-based periodic PM optimization model, which uses the posterior estimates to simulate the number of operational equipment failures, under a given periodic PM policy. Optimal periodic PM policies, under the classical maximum likelihood (ML) and Bayesian estimates are obtained for a few datasets. Limitations of the ML approach are revealed for a dataset from the literature, in which the use of ML estimates of the parameters, in the maintenance optimization model, fails to capture a trivial optimal PM policy. Finally, we introduce a single-stage and a two-stage formulation of the risk-averse periodic PM optimization model, with imperfect PMs and minimal CMs. Such models apply to a class of complex equipment with many parts, operational failures of which are addressed by replacing or repairing a few parts, thereby not affecting the failure rate of the equipment under consideration. For general values of PM age reduction factors, we provide sufficient conditions to establish the convexity of the first and second moments of the number of failures, and the risk-averse expected total maintenance cost, over a finite planning horizon. For increasing Weibull rates and a general class of increasing and convex failure rates, we show that these convexity results are independent of the PM age reduction factors. In general, the optimal periodic PM policy under the single-stage model is no better than the optimal two-stage policy. But if PMs are assumed perfect, then we establish that the single-stage and the two-stage optimization models are equivalent. / text