Low frequency oscillations are detrimental to the goals of maximum power transfer and optimal power system security. A contemporary solution to this problem is the addition of power system stabilizers to the automatic voltage regulators on the generators in the power system. The damping provided by this additional stabilizer provides the means to reduce the inhibiting effects of the oscillations. This thesis is an investigation of the use of synchronized phasor measurements as input signals for power system stabilizers installed on the generators of a two-area, 4-machine test power system. A remote measurement feedback controller has been designed and placed in the test power system. Synchronized phasor measurements from optimally sited measurement units were shown to improve the damping of low-frequency inter-area oscillations present in the test system when the proposed controller was included in the generator feedback control loop. The benefit of the damping of these oscillations was evident through the ability to increase the tie-line power flowing in the test system once the proposed control scheme was implemented. Time-domain simulations were used to verify the robustness of the proposed control during severe events, such as a short- circuit or sudden large variations of load. / Master of Science

Power system stabilizers (PSSs) provide the most economical way to improve damping of electro-mechanical oscillations in electrical power systems. Synchrophasor technology enables the use of remotely measured signals in the PSS allowing for greater flexibility in the design of the PSS. Issues related to the transmission of remote signals should be addressed before implementing such systems in practice. This study investigates two of the data transmission issues: (i) delays, and (ii) data dropout; using a synchrophasor-based PSS designed for a two-area four-generator power system model. A time delayed system is modeled using discrete transformation and the effect of the constant delay on the control action of improving damping of an electro-mechanical oscillation is determined analytically. The effect of random delays and data dropout is investigated using non-linear simulations considering viable remedies to overcome these effects. This research also identifies effective means of using synchrophasor signals for improving the performance of PSSs. Primarily, this research introduces a novel control design algorithm based on eigenstructure assignment that could utilize remotely measured signals to design a robust PSS considering different operating conditions at the design stage. Remote signals could be used as additional inputs to the controller, which introduces extra degrees of freedom. In eigenstructure assignment, these additional degrees of freedom are used to assign eigenvalues and eigenvectors to have adequate damping performance of the system over different operating conditions. The algorithm is formulated as a derivative-free non-linear optimization problem and solved using a single step of optimization by eliminating the use of eigenvalue sensitivities. The proposed algorithm is tested for the 68 bus model of the interconnected New England test system and New York power system. Three different control configurations that use local and remote signals are considered in the design. The algorithm is solved using non-linear simplex optimization considering different initial points for seeking a global solution. Delays in the remote signals are also incorporated into the design. The designed controllers are verified in a non-linear simulation platform. Finally, the reliability of synchrophasor-based PSS is discussed in brief. / February 2016

O problema de modos intra-planta em sistemas de potência é caracterizado pela oscilação dos geradores de uma mesma usina uns contra os outros. Estes modos são geralmente bem amortecidos, mas uma sintonia inadequada dos parâmetros dos PSSs (Power System Stabilizers), visando fornecer um amortecimento aos modos locais, por exemplo, pode reduzir o amortecimento dos modos intra-planta. Esta possibilidade pode ser evitada por uma sintonia cuidadosa dos estabilizadores, em um modelo que seja capaz de representar os modos intra-planta. Este processo de sintonia pode ser tedioso e demorado, exigindo muitas horas de trabalho de um especialista. Neste trabalho, apresentamos um algoritmo computacional capaz de realizar esse processo, com uma intervenção mínima do projetista (reduzindo, portanto, o esforço do engenheiro projetista na sintonia do PSS e deixando que o computador faça de maneira eficiente) e aplicamos este algoritmo para encontrar uma sintonia adequada de PSSs para o amortecimento dos modos local e intra-planta coexistentes no mesmo sistema. Como mostrado neste trabalho, o algoritmo é capaz de sintonizar os PSSs para varias condições de operação de uma só vez, o que pode também resultar em uma melhor sintonia quando comparado com abordagens seqüenciais de projeto. / The problem of intra-plant modes is characterized by the oscillation of the machines within a power station against each other. These modes are usually well-damped, but improper settings for the parameters for power system stabilizers (PSSs), aiming at enhancing the damping of local modes, for example, can reduce the damping of the intra-plant modes. This possibility must be avoided by a careful tuning of the stabilizers, over a model that is able to represent the intra-plant modes. This tuning process may be involved and time-consuming, requiring many hours of work from a specialist. In this paper, we present a computerized algorithm that is capable of performing this process with minimum intervention of the human designer (therefore alleviating the burden of PSS tuning for the engineer and placing most of it on the computer) and apply it to find a PSS tuning to damp both local and intra-plant modes of the same plant. As shown in the paper, the algorithm is capable of tuning PSSs for several operating conditions at once, which may also result in better tuning when compared to sequential approaches.

O presente trabalho se propõe a elaborar algoritmos para controle robusto de sistemas de potência. O modelo de sistema de potência multimáquinas utilizado é o de pequenas perturbações, e o objetivo principal é aumentar o amortecimento dos autovalores críticos do sistema, garantindo sua estabilidade e desempenho em diversas condições operativas. Para isso, são utilizadas as Desigualdades Matriciais Lineares (ou LMI\'s), muito adequadas ao tratamento de problemas de controle robusto por sua flexibilidade e possibilidade de agrupamento de diversos requisitos de desempenho. São propostos, entre outros, três algoritmos fundamentais para controle robusto: dois estão relacionados ao controle descentralizado e com controladores de estrutura fixa, o que é muito comum na indústria de potência atualmente, e o outro está relacionado ao controle hierarquizado, que consiste na integração de várias camadas de controle utilizando sinais remotos. Os algoritmos de controle descentralizado propostos são inovadores, pois ambos os métodos permitem a utilização de controladores de estrutura fixa (qualquer que seja ela), e o algoritmo de controle hierarquizado propõe uma estrutura de controle inédita que utiliza aproximações de Padé de diversas ordens para representar os atrasos de comunicação no sistema. Durante a fase de projeto, pode-se escolher o atraso de comunicação, bem como a ordem da aproximação de Padé desejada. Nos algoritmos de controle robusto descentralizado, realizamos uma minimização da norma da matriz de ganhos estáticos do controlador, o que impede que o resultado do algoritmo sejam parâmetros de valores muito elevados e infactíveis para os controladores. A técnica utilizada para os três controladores propostos é o posicionamento de pólos, o que garante que os autovalores do sistema de potência em malha fechada estejam numa dada região do plano complexo, relacionada ao amortecimento mínimo desejado para os autovalores do sistema. Os testes e simulações realizados para validação dos algoritmos de controle robusto foram feitos em ambiente MATLAB, e foram utilizados diversos sistemas de potência: sistema New England de 39 barras e 9 geradores, sistema New England de 69 barras e 16 geradores e sistema New England de 39 barras utilizando modelos de termogeradores. Os testes sugerem que as técnicas propostas são eficazes, pois todas elas garantem boas taxas de amortecimento para os sistemas de potência utilizados. Ao final, simulações não-lineares comprovam a eficácia e a eficiência de um dos controladores projetados para o sistema New England de 39 barras. / The aim of this work is to elaborate robust control algorithms to power systems. The mathematical model employed to describe the multimachine power system is that used in small signal studies, and the main goal is to increase the damping of the critical eigenvalues of the system, guaranteeing its stability and performance in various operating conditions. To do this, we apply the Linear Matrix Inequalities (or simply LMI\'s), suitable to deal with robust control problems due to its flexibility and possibility to group many performance requisites. We propose three robust control algorithms: two of them are related to decentralized control with controllers of predefined structure, which are commonly used in the power industry, and the other one is related to the hierarchized control, which consists on the integration of various controllers layers using remote signals. The decentralized robust control algorithms proposed are novel, because both methods make possible the development of controllers of pre-defined structure, and the hierarchized control algorithm suggests a novel control structure that uses Padé approximations of different orders to represent the communication delays in the system. During the design, we can choose the communication delay, as well as the order of the Padé approximation desired. The decentralized robust control algorithms solve minimization problems over the controller gain matrix norm, which guarantees that the final values of the controller\'s parameters will not be much high and impracticable. The technique employed for the three types of controllers proposed is the pole placement, which ensures that the eigenvalues of the closed loop power system will be in a certain region of the complex plane, related to the minimum damping required for the system. Tests and simulations are done in MATLAB to validate the robust control algorithms, and we apply these algorithms to various power systems: 39-bus 9-machine New England power system, 69-bus 16-machine New England power systems and 39-bus New England power system with thermo machine models. The tests suggest that the proposed techniques work well, once all of them guarantee good damping rates to the power systems considered. To complete the tests round, nonlinear simulations proof the efficiency of the controllers designed for the 39-bus New England power system.

O problema de modos intra-planta em sistemas de potência é caracterizado pela oscilação dos geradores de uma mesma usina uns contra os outros. Estes modos são geralmente bem amortecidos, mas uma sintonia inadequada dos parâmetros dos PSSs (Power System Stabilizers), visando fornecer um amortecimento aos modos locais, por exemplo, pode reduzir o amortecimento dos modos intra-planta. Esta possibilidade pode ser evitada por uma sintonia cuidadosa dos estabilizadores, em um modelo que seja capaz de representar os modos intra-planta. Este processo de sintonia pode ser tedioso e demorado, exigindo muitas horas de trabalho de um especialista. Neste trabalho, apresentamos um algoritmo computacional capaz de realizar esse processo, com uma intervenção mínima do projetista (reduzindo, portanto, o esforço do engenheiro projetista na sintonia do PSS e deixando que o computador faça de maneira eficiente) e aplicamos este algoritmo para encontrar uma sintonia adequada de PSSs para o amortecimento dos modos local e intra-planta coexistentes no mesmo sistema. Como mostrado neste trabalho, o algoritmo é capaz de sintonizar os PSSs para varias condições de operação de uma só vez, o que pode também resultar em uma melhor sintonia quando comparado com abordagens seqüenciais de projeto. / The problem of intra-plant modes is characterized by the oscillation of the machines within a power station against each other. These modes are usually well-damped, but improper settings for the parameters for power system stabilizers (PSSs), aiming at enhancing the damping of local modes, for example, can reduce the damping of the intra-plant modes. This possibility must be avoided by a careful tuning of the stabilizers, over a model that is able to represent the intra-plant modes. This tuning process may be involved and time-consuming, requiring many hours of work from a specialist. In this paper, we present a computerized algorithm that is capable of performing this process with minimum intervention of the human designer (therefore alleviating the burden of PSS tuning for the engineer and placing most of it on the computer) and apply it to find a PSS tuning to damp both local and intra-plant modes of the same plant. As shown in the paper, the algorithm is capable of tuning PSSs for several operating conditions at once, which may also result in better tuning when compared to sequential approaches.

Η παρούσα διπλωματική εργασία έχει ως στόχο την αντιμετώπιση των ηλεκτρομηχανικών ταλαντώσεων οι οποίες εμφανίζονται σε μία σύγχρονη γεννήτρια παραγωγής Ηλεκτρικής Ενέργειας μετά από διαταραχές. Ο συμβατικός έλεγχος για τη διατήρηση της μηχανής σε συγχρονισμό μετά από ξαφνικές αλλαγές φορτίου, βραχυκυκλωμάτων, κλείσιμο διακοπτών ή οποιασδήποτε κατάστασης που μπορεί να προκαλέσει αστάθεια στο Σύστημα της Ηλεκτρικής Ενέργειας, γίνεται με χρήση ελεγκτικών διατάξεων Σταθεροποιητών Συστημάτων Ισχύος σε συνδυασμό με τον Αυτόματο Ρυθμιστή Τάσης (ΑΡΤ/ΣΣΙ). Σκοπός της εργασίας αυτής είναι να σχεδιαστούν και να ρυθμιστούν κατάλληλα οι διατάξεις αυτές, ώστε να εξασφαλίζεται η απόσβεση των ηλεκτρομηχανικών ταλαντώσεων που εμφανίζονται ανάμεσα στην γεννήτρια και το υπόλοιπο σύστημα. Στην εργασία αυτή, αρχικά γίνεται μια εισαγωγή στα είδη των ηλεκτρομηχανικών ταλαντώσεων και την ευστάθεια για δυναμικά Συστήματα Ηλεκτρικής Ενέργειας. Στη συνέχεια αναπτύσσεται το δυναμικό μοντέλο ενός απλού συστήματος μιας γεννήτριας άπειρου ζυγού βασισμένο στο απλοποιημένο μοντέλο 4ης τάξης της σύγχρονης μηχανής. Επειδή το μοντέλο αυτό είναι μη γραμμικό προχωράμε στην εξαγωγή του γραμμικοποιημένου μοντέλου που θα μας βοηθήσει για τον σχεδιασμό του κατάλληλου ελεγκτή. Αξιοποιώντας ιδιότητες του μοντέλου παρουσιάζεται μια συστηματική μέθοδος σχεδίασης του Σταθεροποιητή Συστήματος Ισχύος που είναι βασισμένη στη λογική των ολοκληρωτικών υπολοίπων. Τέλος με τη βοήθεια του λογισμικού SIMULINK του MATLAB προσομοιώνεται το σύστημα σύγχρονης γεννήτριας συνδεδεμένης σε άπειρο ζυγό, που ελέγχεται με την χρήση του Αυτόματου Ρυθμιστή Τάσης και του Σταθεροποιητή Συστήματος Ισχύος σε κατάσταση τυπικής φόρτισης. Εφαρμόζοντας διαταραχές στο σύστημα παρατηρείται η απόκριση του συστήματος και εκτιμάται η λειτουργία του ελεγκτή. / This thesis aims to address the electromechanical oscillations which appear in a synchronous generator after disturbances. The conventional control for maintaining the machine synchronized after sudden load changes, short circuits, switching or any condition which may cause instability phenomena, is achieved by the use of control circuits such as Power System Stabilizers combined with the Automatic Voltage Regulator ( PSS / AVR). The purpose of this work is to design and configure properly these control circuits to ensure the reduction of electromechanical oscillations that occur between the generator and the rest of the system. In the beginning this thesis, an introduction of the types of power system electromechanical oscillations and stability is being discussed. Afterwards, the dynamic model of a simple system of a generator infinite-bus based on simplified 4th order of synchronous machine is being developed. Due to the model nonlinearities, we export the linearized model which helps us to design a suitable controller. Taking into account the model properties, we provide a systematic method for designing a Power System Stabilizer based on the residues method. Finally, using the MATLAB-SIMULINK software, the synchronous generator infinite-bus system is simulated which is controlled by an Automatic Voltage Regulator and a Power System Stabilizer. After applying disturbances, the system response is driven and analyzed along with the controller functioning.

Orientador: Percival Bueno de Araujo / Resumo: Neste trabalho, uma técnica baseada na Busca em Vizinhança Variável Básica é apresentada para realizar o ajuste coordenado dos parâmetros dos controladores suplementares de amortecimento Thyristor Controlled Series Capacitor - Power Oscillation Damping e Estabilizadores de Sistemas de Potência, a fim de garantir a estabilidade a pequenas perturbações de sistemas elétricos de potência. A estratégia do método de ajuste proposto consiste em explorar sistematicamente estruturas de vizinhança atrelada a uma etapa de busca local, tornando possível a obtenção de soluções ótimas e a manutenção da capacidade de evitar a estagnação em um ótimo local. Um modelo do TCSC por injeção de corrente é apresentado e seus coeficientes de sensibilidade de corrente são deduzidos para incorporação ao Modelo de Sensibilidade de Corrente, que é utilizado para representar o sistema elétrico de potência. Com a inclusão da modelagem dos controladores de amortecimento, simulações são realizadas em dois sistemas testes, conhecidos como sistema Simétrico de Duas Áreas e sistema New England. Os resultados obtidos são analisados para melhor compreensão do comportamento do sistema elétrico de potência quando submetido a uma pequena perturbação e da influência dos controladores de amortecimento neste cenário. Os parâmetros dos controladores são ajustados pelo algoritmo Particle Swarm Optimization, por um Algoritmo Genético e, também, pelo método proposto neste trabalho. Os desempenhos individuais dos métodos d... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work, a technique based on Basic Variable Neighborhood Search is presented to perform the coordinated tuning of the parameters of the supplementary damping controllers Thyristor Controlled Series Capacitor - Power Oscillation Damping and Power System Stabilizers in order to guarantee the small-signal stability of the electric power systems. The strategy of the proposed tuning method consists in systematically exploring neighborhood structures followed by a local search stage, making it possible to obtain optimal solutions and to maintain the ability to avoid stagnation in a local optimum. A current injection model for the TCSC is presented and its current sensitivity coefficients are deduced for incorporation into the Current Sensitivity Model, which is used to represent the electric power system. With the inclusion of the damping controllers modeling, simulations are performed on two test systems, known as the Two-Area Symmetric system and New England system. The results obtained are analyzed to better understand the behavior of the electric power system when subjected to a small disturbance and the influence of the damping controllers in this scenario. The controllers parameters are tuned by the Particle Swarm Optimization algorithm, by a Genetic Algorithm and also by the method proposed in this work. The individual performances of the tuning methods are compared in order to conclude on the technique best suited for this type of problem, including the analysis of a ... (Complete abstract click electronic access below) / Doutor

O presente trabalho se propõe a elaborar algoritmos para controle robusto de sistemas de potência. O modelo de sistema de potência multimáquinas utilizado é o de pequenas perturbações, e o objetivo principal é aumentar o amortecimento dos autovalores críticos do sistema, garantindo sua estabilidade e desempenho em diversas condições operativas. Para isso, são utilizadas as Desigualdades Matriciais Lineares (ou LMI\'s), muito adequadas ao tratamento de problemas de controle robusto por sua flexibilidade e possibilidade de agrupamento de diversos requisitos de desempenho. São propostos, entre outros, três algoritmos fundamentais para controle robusto: dois estão relacionados ao controle descentralizado e com controladores de estrutura fixa, o que é muito comum na indústria de potência atualmente, e o outro está relacionado ao controle hierarquizado, que consiste na integração de várias camadas de controle utilizando sinais remotos. Os algoritmos de controle descentralizado propostos são inovadores, pois ambos os métodos permitem a utilização de controladores de estrutura fixa (qualquer que seja ela), e o algoritmo de controle hierarquizado propõe uma estrutura de controle inédita que utiliza aproximações de Padé de diversas ordens para representar os atrasos de comunicação no sistema. Durante a fase de projeto, pode-se escolher o atraso de comunicação, bem como a ordem da aproximação de Padé desejada. Nos algoritmos de controle robusto descentralizado, realizamos uma minimização da norma da matriz de ganhos estáticos do controlador, o que impede que o resultado do algoritmo sejam parâmetros de valores muito elevados e infactíveis para os controladores. A técnica utilizada para os três controladores propostos é o posicionamento de pólos, o que garante que os autovalores do sistema de potência em malha fechada estejam numa dada região do plano complexo, relacionada ao amortecimento mínimo desejado para os autovalores do sistema. Os testes e simulações realizados para validação dos algoritmos de controle robusto foram feitos em ambiente MATLAB, e foram utilizados diversos sistemas de potência: sistema New England de 39 barras e 9 geradores, sistema New England de 69 barras e 16 geradores e sistema New England de 39 barras utilizando modelos de termogeradores. Os testes sugerem que as técnicas propostas são eficazes, pois todas elas garantem boas taxas de amortecimento para os sistemas de potência utilizados. Ao final, simulações não-lineares comprovam a eficácia e a eficiência de um dos controladores projetados para o sistema New England de 39 barras. / The aim of this work is to elaborate robust control algorithms to power systems. The mathematical model employed to describe the multimachine power system is that used in small signal studies, and the main goal is to increase the damping of the critical eigenvalues of the system, guaranteeing its stability and performance in various operating conditions. To do this, we apply the Linear Matrix Inequalities (or simply LMI\'s), suitable to deal with robust control problems due to its flexibility and possibility to group many performance requisites. We propose three robust control algorithms: two of them are related to decentralized control with controllers of predefined structure, which are commonly used in the power industry, and the other one is related to the hierarchized control, which consists on the integration of various controllers layers using remote signals. The decentralized robust control algorithms proposed are novel, because both methods make possible the development of controllers of pre-defined structure, and the hierarchized control algorithm suggests a novel control structure that uses Padé approximations of different orders to represent the communication delays in the system. During the design, we can choose the communication delay, as well as the order of the Padé approximation desired. The decentralized robust control algorithms solve minimization problems over the controller gain matrix norm, which guarantees that the final values of the controller\'s parameters will not be much high and impracticable. The technique employed for the three types of controllers proposed is the pole placement, which ensures that the eigenvalues of the closed loop power system will be in a certain region of the complex plane, related to the minimum damping required for the system. Tests and simulations are done in MATLAB to validate the robust control algorithms, and we apply these algorithms to various power systems: 39-bus 9-machine New England power system, 69-bus 16-machine New England power systems and 39-bus New England power system with thermo machine models. The tests suggest that the proposed techniques work well, once all of them guarantee good damping rates to the power systems considered. To complete the tests round, nonlinear simulations proof the efficiency of the controllers designed for the 39-bus New England power system.

In the Nordic power network, the existence of poorly damped low-frequency inter-area oscillations (LFIOs) has long affected stability constraints, and thereby, limited power transfer capacity. Adequate damping of inter-area modes is, thus, necessary to secure system operation and ensure system reliability while increasing power transfers. Power system stabilizers (PSS) is a prevalent means to enhance the damping of such modes. With the advent of phasor measurement units (PMUs), it is expected that wide-area damping control (WADC), that is, PSS control using wide-area measurements obtained from PMUs, would effectively improve damping performance in the Nordic grid, as well as other synchronous interconnected systems. Numerous research has investigated one ``branch'' of the problem, that is, PSS design using various control schemes. Before addressing the issue of controller design, it is important to focus on developing proper understanding of the ``root'' of the problem: system-wide oscillations, their nature, behavior and consequences. This understanding must provide new insight on the use of PMUs for feedback control of LFIOs. The aim of this thesis is, therefore, to lay important concepts necessary for the study of power system small signal stability analysis that considers the availability of synchrophasors as a solid foundation for further development and implementation of ideas and related applications. Particularly in this study, the focus is on the application addressed damping controller design and implementation. After a literature review on the important elements for wide-area damping control (WADC), the thesis continues with classical small signal stability analysis of an equivalent Nordic model; namely, the KTH-NORDIC32 which is used as a test system throughout the thesis. The system's inter-area oscillations are identified and a sensitivity analysis of the network variables directly measured by synchrophasors is evaluated. The concept of network modeshapes, which is used to relate the dynamical behavior of power systems to the features of inter-area modes, is elaborated. Furthermore, this network modeshape concept is used to determine dominant inter-area oscillation paths, the passageways containing the highest content of the inter-area oscillations. The dominant inter-area paths are illustrated with the test system. The degree of persistence of dominant paths in the study system is determined through contingency studies. The properties of the dominant paths are used to construct feedback signals as input to the PSS. Finally, to exemplify the use of the dominant inter-area path concept for damping control, the constructed feedback signals are implemented in a PSS modulating the AVR error signal of a generator on an equivalent two-area model, and compared with that of conventional speed signals.

In this report, the effect that a higher penetration ofrenewable energy sources has on electric power grid stability isevaluated. The report also compares different methods of stabilizingan unstable grid. The model used is a two-area four-machinesystem and the main objective is to stabilize the synchronousgenerators such that they revert back to synchronism afterbeing subjugated to a small signal disturbance. The stabilizationmethods consists of supplementary Power System Stabilizers(PSSs) complementing the exciter systems of the synchronousmachines, as well as two types of converter-based controllers inthe renewable energy source: Grid-Following (GFL) convertersand Grid-Forming (GFM) converters. The results show thata system with renewable energy sources is more sensitive todisturbances and has a larger rotor angle deviation from a steadystate when using only GFLs compared to the conventional gridwithout PSSs. It is also found that a conventional grid requiressupplementary PSSs to be stable. This is also the case for asystem with renewable energy controlled by GFL. The systemwith GFM controllers does however not need supplementary PSSto be stable. This leads to the conclusion that GFM is morepreferable than GFL to control a grid with a higher penetrationof renewable energy. / I denna rapport utvärderas hur en högre andel förnybara energikällor påverkar stabiliteten i elnät, och jämför också olika metoder för att stabilisera ett instabilt nät. Modellen som används var ett två-områdes-fyrmaskinsystem och huvudsyftet är att stabilisera synkrongeneratorerna så att de återgår till synkronism efter att ha utsatts för en liten småsignalsstörning. Stabiliseringsmetoderna består av kompletterande Power System Stabilizers (PSS:er) som kompletterade exciteringssystemen i synkronmaskinerna, samt två typer av omvandlarbaserade styrenheter i den förnybara energikällan: Grid-Following (GFL)-omvandlare och Grid-Forming (GFM)omvandlare. Resultaten visar att ett system med förnybara energikällor är mer känsligt för störningar och har en större rotorvinkelavvikelse från ett stationärt tillstånd när GFL-kontroller används jämfört med det konventionella nätet utan PSS:er. Det visar sig också att ett konventionellt nät kräver kompletterande PSS:er för att vara stabilt. Detta är också fallet för ett system med förnybar energi som enbart kontrolleras av GFL-omvandlare. Systemet med GFM-omvandlare behöver dock inte kompletterande PSS för att vara stabilt. Detta leder till slutsatsen att GFM är mer att föredra än GFL för att kontrollera ett nät med högre andel förnybar energi. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm