The plans to reduce the energy-related greenhouse gas emissions stimulate the deployment of electronically interfaced renewable resources. The increased penetration of such intermittent sources together with phasing conventional power plants out and the installation of High Voltage Direct Current (HVDC) links for long-distance more efficient transmission, reduces the stored inertia in any electrical grid. This leads to a more vulnerable power system and increases the significance of studying the corresponding stability aspects. Decreasing the inertial response of a power system deteriorates the quality of both frequency and rotor-angle stability which are the dynamics of interest in this study. The thesis explores the role of the location of low inertia on varying the power system’s dynamics. This is to be conducted in isolation of all other factors that could affect the study outcomes, such as dealing with the same system’s inertia value upon lowering the inertia in different locations. To accomplish this objective, it is essential to analyze the inertia distribution of the examined power system following the alterations of inertia reduction location. Accordingly, an inherently previous work methodology, that estimates the relative distance of the system’s components to Center Of Inertia (COI), is utilized throughout this study. Both frequency response and small-signal stability are analyzed in light of the inertia distribution results. The thesis examines two different power systems, a small two-area model and a bigger more realistic power system. The former model, known as Kundur model, helps in building a conceptual process to apply the methodology and to benchmark the dynamics of interest. While the latter is a reduced model of the Swedish transmission grid, known as Nordic 32 model. Different scenarios of low inertia are considered to capture the current trend of integrating more Renewable Energy Sources (RES) and phasing out more conventional plants. DIgSILENT Powerfactory is the weapon of choice in this study. It is utilized to assess both the frequency stability by performing electromechanical transients’ simulations, and small-signal stability following modal analysis simulations.  Results show that the alterations of low inertia location are associated with variations in Instantaneous Frequency Deviation (IFD), Rate Of Change Of Frequency (ROCOF) and the damping ratio of the most critical inter-area oscillation mode. These variations have different levels of significance. Variations of the latter two metrics have the most considerable effects from the stability’s perspective. They can be utilized to prioritize the phasing out process of the conventional power plants, and to choose one of the scenarios of a specific low inertia location over the others. This helps in fulfilling proper long-term planning and short-term operation from the system operator’s perspective.

The increasing amount of renewable energy sources is applying more and more pressure on today’s power system. Additionally, plannable sources of energy, which are mostly non-renewable, are being decommissioned at a high rate to combat climate change. The decommissioning of non-renewable producers and the increasing number of intermittent sources of energy are causing an increasingly volatile power system. In addition to the lack of plannable production, the inertia from synchronously rotating machines is decreasing due to the lack of contribution from renewable sources. The inertia of a power system assists in slowing down large frequency changes. When a notably large difference between production and consumption occurs in a power system with low inertia, components which can quickly counteract these effects by supplying the system with active power, are needed. The low inertia can also cause problems to the synchronicity of the synchronously rotating machines in the system, namely the rotor angle stability. A lack of rotorangle stability can cause the synchronicity of the synchronously rotating machines to be questioned. Fast frequency response units supply the power system with active power for a short period of time to reduce the rate of change of frequency and frequency deviation, which in turn allows the self-regulating units more time to adjust their production. Furthermore, these units can improve rotor angle stability. Such units can consist of batteries which are both serially and parallel connected with their associated control unit. This thesis aims to, with the help of the power system analysis program PowerFactory, and its associated dynamic simulation tools, formulate a methodology which can be used in power system models to locate the best placement for fast frequency response units. The results show that the formulated methodology can be used to find the best position of fast frequency response units for frequency deviation-, rate of change of frequency- and rotor angle stability support.

This research argues that a diesel-based isolated electrical system can be optimized byintegrating a high share of solar photovoltaic (PV) generation and that the frequencystability of such system can be improved by including the PV participation in frequencyregulation. A case study is developed in order to explore an island’s expansion of theinstalled generating capacity and its optimization. This study uses the tool HOMER tosolve the optimization problem and PowerFactory to verify the frequency stability of theproposed system. The PV integration allows for a reduction of diesel fuel consumption,emissions and generation costs. Additionally, in high PV penetration scenarios, the reducedinertia in such systems can lead to high frequency deviations that may trip the systemprotection. The study demonstrates that the instantaneous frequency deviation after a loadand generation imbalance can be reduced by designing the PVs to operate with an allocatedreserve and a decentralized time-based secondary frequency control. The frequency stabilitywas achieved after different disturbance scenarios under high PV penetration and reducedavailable inertia, indicating that high PV integration is economically and technically feasiblein small island grids. / I detta examensarbete studeras hur ett dieselbaserat och isolerat elsystem kan optimeras genom att integrera en hög andel solceller (PV) i elproduktionen och att frekvensstabilitet kan förbättras när PV användas i regleringen. En fallstudie har utvecklats under denna forskning för att analysera en ökning av den installerade generationskapacitet vid en ö samt hur detta kan optimeras. I denna studie användas verktyget HOMER för modeloptimering och PowerFactory för att testa den optimerade systemfrekvens stabilitet. Med PV generation kan diesel konsumption, utsläpp och kostnader minskas för hela systemet. En hög andel PV i generationen reducerar elsystemet totala svängmassa vilket kan ledda till avvikelser i systemfrekvensen som kan ursaka att skyddsystem aktiveras. Studien demonstrerar att den momentana systemavvikelsen efter en obalans kan reduceras genom att designa PV i systemet med en allokerad reserv och en decentraliserad och tidsbaserad sekundär frekvensreglering. Frekvensstabiliteten nåddes i olika obalans scenarier med hög andel solcellgeneration och misnkat svängsmassa. Detta tyder på att en hög andel PV integration är både ekonomisk- och tekniskt möjligt i mindre elsystem.

In order to meet the increasing demand for sustainable transportation, trains need to run with tighter schedules, more departures and more trains in depot. Multiple trains in depot has been linked to low frequency instability at many locations around the world. The instability originates in the interaction between the infrastructure and trains, specifically the line converter module (LCM). The phenomenon has been studied during the last two decades. Today there are a number of methods used to analyse low frequency stability, although these methods are usually slow and cumbersome. In this project a modelling approach is proposed for a linear small-signal DQ-frame admittance model of the LCM. The model describes the relationship of the low frequency oscillations between the line voltage and line current. Similar linear models have been derived previously, although the design of the specific train modelled is in part significantly different from the design of the trains modelled previously. The main difference is in the DQ-transformation for the phase locked loop (PLL), which in this thesis is implemented with a DFT-based method, and the implementation of the current controller (CC) which in this thesis is implemented in the stationary reference frame. The LCM and infrastructure (modelled as an impedance) is then analysed as a feedback loop using dominant poles analysis, regularly used in control theory. The result from the proposed model was evaluated using methods that are common in the industry. Furthermore, as the LCM is a complex system and the impact of different components and control parameters is not fully understood, the proposed model is used to examine how changing different parameters affect the overall stability of the system. The correlation between the results from the proposed model and the methods used for evaluation implies that the modelling approach is accurate. The two main benefits of the proposed model is that the method is much faster than most other methods for low frequency analysis, the proposed model is useful for testing different parameter configurations and changes in the design of the LCM. / För att möta den ökande efterfrågan på hållbar transport, behöver tåg idag köras med stramare tidtabeller, fler avgångar och fler tåg i depå. Flera tåg i depå har kopplats till lågfrekvent instabilitet på många platser runt om i världen. Instabiliteten har sitt ursprung i interaktionen mellan infrastrukturen och tågen, särskilt nätströmriktaren (LCM). Fenomenet har studerats under de senaste två decennierna. Idag finns det ett antal metoder som används för att analysera lågfrekvent stabilitet, dock är dessa metoder vanligtvis är långsamma och besvärliga. Detta projekt beskriver en modelleringsmetod lågfrekvenssvängningar mellan linjespänningen och linjeströmmen. Liknande linjära modeller har härletts tidigare, skiljer sig utformningen av det specifika tåget modellerad i denna avhandling från de tåg som modellerats tidigare i vissa design val. Den största skillnaden ligger i DQ-transformationen för den synkroniseringsregulatorn (PLL), som i denna avhandling är implementerad med en DFT-baserad metod, och implementeringen av strömregulatorn (CC) som i denna uppsats implementeras i den stationära referensramen. LCM tillsammans med infrastruktur (modellerad som en impedans) analyseras sedan som en stängd återkoppling där det stängda systemets poler härleds. Resultatet från den föreslagna modellen utvärderades med metoder som är vanliga i branschen. Dessutom, eftersom LCM är ett komplext system och effekten av olika komponenter och styrparametrar inte är helt förstod, används modellen för att undersöka hur förändringar i olika parametrar påverkar hela systemets stabilitet. Korrelationen mellan resultaten från det föreslagna modell och de metoder som används för utvärdering av lågfrekvent stabilitet idag innebär att modelleringsmetoden är lovande. De metoden är mycket snabbare än de flesta andra metoder för lågfrekvent analys och att den föreslagna modellen är användbar för att testa olika parameterkonfigurationer och förändringar i utformningen av LCM.

The Nordic power system is in a changing phase, with more power electronic interfaced connections, and HVDC connections to other synchronous areas, which impacts the frequency quality. This is a challenge for the transmission system operator of Sweden, Svenska Kraftnät, who, with the other Nordic transmission system operators, is responsible for the physical balancing of the Nordic power system. To ensure that the grid can maintain stable operation when power imbalances or a disturbance occur, the frequency quality is important to evaluate. According to the current measurement of frequency quality, minutes outside of the standard frequency band, the frequency quality in the Nordic power system has been deteriorating. The current measurement does not capture what impact the frequency quality and needs to be redefined, with more precise measurements, for Svenska Kraftnät to be able to take necessary actions to ensure stability of the power system. Therefore, the purpose of this project is to determine which key performance indices, KPIs, can be used to develop the definition of frequency quality, and which system parameters are captured by the different KPIs. This project is executed with simulations in Matlab/Simulink to determine the impact five system parameters have on 15 different KPIs, and the results from the simulations are validated with historical data. The results indicate that all system parameters can be captured with KPIs, but after validation with historical data only two system parameters, which correlated with four KPIs, were deemed to be valid. The amount of FCR-N energy activated can be captured with the standard deviation of frequency, frequency area, and number of FCR-D activations. The kinetic energy can be captured by the standard deviation of RoCoF. The KPIs are recommended to be used to identify, and measure, the impact of new technical requirements for frequency control, and how the frequency stability is impacted by changes in the system. The conclusion is that four key performance indices are recommended to improve the definition of frequency quality, and further research is recommended to further define the concept of frequency quality. / För tillfället sker stora förändringar i det nordiska elsystemet. Fler produktionsanläggningar och industrier ansluts med kraftelektronik och fler HVDC-anslutningar byggs till andra synkronområden, vilket har stor inverkan på frekvenskvalitén. Detta leder till nya utmaningar för det svenska transmissionsnätets systemansvariga myndighet, Svenska Kraftnät, som gemensamt med sina nordiska motsvarigheter är ansvariga för den fysiska balanseringen i det nordiska synkronområdet. Det är viktigt att kontinuerligt följa upp frekvenskvalitén i transmissionsnätet så att stabil drift kan garanteras både vid mindre obalanser eller i händelse av större störningar. Det nuvarande nyckeltalet för uppföljning av frekvenskvalité, minuter utanför normalbandet, indikerar att frekvenskvalitén i det nordiska synkronområdet har blir sämre de senaste åren. Det nuvarande nyckeltalet indikerar inte vad som påverkar frekvenskvalitén och behöver omdefinieras med mer precisa nyckeltal för att Svenska Kraftnät ska kunna vidta nödvändiga åtgärder för att garantera en stabil drift av transmissionnätet. Syftet med examensarbetet är att definiera nya nyckeltal för att beskriva frekvenskvalité samt undersöka vilka systemparametrar som fångas av de olika nyckeltalen. I detta projekt har simuleringar utförts i Matlab/Simulink för att bestämma den inverkan fem olika systemparametrar har på 15 olika nyckeltal. Resultaten från simuleringar valideras med historisk data. Resultaten från simuleringen indikerar att de fem systemparametrarna kan fångas av olika kombinationer av de föreslagna nyckeltalen, men efter validering med historisk data bedöms enbart två systemparametrar fångas av totalt fyra nyckeltal. Systemparametern aktiverad FCR-N energi fångas av tre nyckeltal: frekvensens standardavvikelse, frekvensarea och antal FCR-D-aktiveringar. Systemparametern kinetisk energi fångas av ett nyckeltal: frekvensderivatans standardavvikelse. De fyra identifierade nyckeltalen kan användas för att identifiera och mäta hur frekvenskvalitén påverkas av nya tekniska krav, samt hur frekvensstabilitet påverkas av förändringar i systemet. Slutsatsen för detta projekt är att fyra nya nyckeltal rekommenderas för att utveckla definitionen av frekvenskvalité. Vidare arbete rekommenderas för att kunna utveckla begreppet vidare.

Mauritius is an isolated island with ambitious targets for renewable energy generation and plans to invest in more solar power. The aim of this study is to assess how the implementation of photovoltaic technologies might affect the frequency stability in Mauritius and thus assess whether solar power can help the country obtain their targets for green energy generation. The research question is answered by conducting a literature study and simulating relevant scenarios in Matlab and Simulink. By simulating the frequency response for a production disturbance with different values for system inertia and PV capacity, the inertia requirements for frequency stability is assessed. Mauritius appears to have a high potential for increasing solar power generation. Based on the simulations, their electrical grid seems to be able to maintain frequency stability with PV capacity corresponding to the generation targets for 2020, 2025 and 2030, even for low amounts of system inertia. However, the significance of these results are called into question because of the varying quality of input data. With more accurate, specific data, the applicability of the results can be improved. Nevertheless, the study can be used as a guideline on how to use the given model to evaluate frequency stability in isolated power systems in island states. Ways to further this study is to evaluate other stability challenges related to PV production such as the reactive power in the system, voltage stability and rotor angle stability. / Mauritius är en isolerad ö som har sett en stor ekonomisk växt de sista åren. För att möta en ökande efterfrågan på el på ett hållbart sätt har Mauritius satt ambitiösa mål för förnybar energiproduktion som bland annat innebär betydande investeringar i solkraft. Målet med denna studie är att utvärdera hur implementeringen av utökad solcellskapacitet skulle kunna påverka frekvensstabiliteten i nätet på Mauritius och således fastställa ifall solenergin kan bidra till deras mål om ökad grön energiproduktion, utan att öka risken för strömavbrott. Frågeställningen besvaras genom att först utföra en litteraturstudie och sedan använda en matematisk modell, utvecklad av Danilo Obradovic från KTH, för att simulera relevanta scenarier i Matlab och Simulink. Simuleringarna visar frekvenssvaret vid produktionsbortfall som relateras till den mängd svängmassa som behövs för att säkerställa frekvensstabilitet vid olika mängder solceller. Litteraturstudien visar att Mauritius har god tillgång på solinstrålning och solceller verkar vara en lämplig teknologi för att utnyttja denna energin. Enligt de simuleringar som genomförts verkar Mauritius kunna bibehålla frekvensensstabilitet om den installerade solcellskapaciteten ökas till de planerade nivåerna i 2020, 2025 och 2030, även för låga värden på systemets svängmassa. Slutsatserna bör dock analyseras kritiskt då indatan som används för simuleringarna är av varierande kvalitet. Med bättre och mer specifik indata kan den föreslagna metodiken och modellen användas för att dra mer relevanta slutsatser för Mauritius. Metodiken som använts i denna studie kan därav ses på som en riktlinje för hur frekvensstabiliteten i isolerade elnät kan undersökas. Vidare kan studien utökas genom att utvärdera sociala och ekonomiska aspekter och även andra stabilitetsfrågor relaterade till en ökad mängd solceller, så som den reaktiva effekten i systemet, spänningsstabilitet och rotorvinkelstabilitet.

Orientador: Carlos Roberto Minussi / Resumo: Nesta pesquisa apresentam-se os principais conceitos gerais de estabilidade elétrica, assim como suas divisões e classificações, onde são desenvolvidas as condições de operação de um sistema elétrico de potência, que são relevantes nos estudos de estabilidade angular do rotor, tensão e frequência. Para os estudos de estabilidade da frequência e de tensão é preciso conhecer os equipamentos como os reguladores de tensão e frequência, em consequência é apresentada a modelagem matemática de vários componentes dinâmicos como o sistema de excitação, estabilizador do sistema de potência (PSS), sistema de regulação de velocidade, sistema de regulação de tensão (AVR), máquina síncrona, turbina a vapor e turbina hidráulica. É necessário a modelagem de eles para projetar seus respectivos controladores. Nesta pesquisa também se faz a introdução ao controlador Fuzzy e controlador PID convencional assim como os métodos de sintonia, depois projetamos um controlador que combine os dois controladores e tenha mais vantagens como o controlador híbrido PID-Fuzzy. Depois de desenvolver a modelagem do regulador de tensão e frequência, fazemos o projeto do controlador PID-Fuzzy, previamente projetado o controle PID. As simulações dos sistemas de regulação de tensão e frequência sem controlador, com controlador PID e com controlador PID-Fuzzy foram realizadas aplicando a ferramenta computacional de Matlab-Simulink no domínio do tempo contínuo e as respostas foram investigadas e discutidas. / Abstract: This research presents the main general concepts of electrical stability, as well as their divisions and classifications, where the operating conditions of an electrical power system are developed, which are relevant in the studies of angular stability of the rotor, voltage and frequency. For frequency and voltage stability studies it is necessary to know equipment such as voltage and frequency regulators, consequently the mathematical modeling of several components is presented as dynamic as the excitation system, power system stabilizer (PSS) , speed regulation system, voltage regulation system (AVR), synchronous machine, steam turbine and hydraulic turbine. We need the modeling of them to design their respective controllers. In this investigation we also do the introduction to the Fuzzy controller and conventional PID controller as well as the tuning methods then we designed a controller that combines the two controllers and has more advantages as the hybrid PID-Fuzzy controller. After developing the modeling of the voltage and frequency regulator, we design the PID-Fuzzy controller, previously designed the PID control. The simulations of the voltage and frequency regulation systems without controller, with PID controller and with PID-Fuzzy controller were performed applying the Matlab-Simulink computational tool in the continuous time domain and the answers were investigated and discussed. / Mestre