This thesis presents a transient stability method using dynamic phasors. This method can be used to investigate low frequency (<5Hz) and sub-synchronous frequency (5Hz-60Hz) oscillations. It has major advantages as compared to traditional transient stability method and EMT method. It allows modeling of higher-frequency oscillation possible using time domain simulations, which is not achievable with conventional method. It also can be simulated at much larger time step as compared to PSCAD/EMTDC simulation. Comparison of the results with traditional model and detailed EMT model are also present, and they show very accurate results at frequency ranges up to 60Hz.

This thesis presents a comprehensive procedure to study sub-synchronous interactions in wind integrated power systems effectively and efficiently. The proposed procedure involves a screening phase and a detailed analysis phase. The screening is performed using a frequency scan and the detailed analysis is performed using small signal stability analysis. To facilitate the small signal analysis, a detailed linearized model of a Type 3 wind power plant is presented in this thesis. The model presented includes the generator, a three-mass drive train model, rotor and grid side converter controller models, converter transformer model and the pitch controller model. To accurately capture the effects of sub-synchronous interactions, the ac network is modelled using dynamic phasors. It is shown that using the proposed procedure, the sub-synchronous interaction between a Type 3 wind power plant and a series compensated line is due to an electrical resonance between the wind power plant generator and the series capacitor. It is also shown that this interaction is highly controllable through the rotor side converter current controllers. This fact will be proven by studying the sub-synchronous interactions in a single machine power system as well as in multi machine power systems. This thesis also presents a sub-synchronous interaction mitigation method using network devices. The performance of an SVC and a STATCOM is evaluated in this thesis. A small signal stability analysis based method will be used to design a sub-synchronous damping controller. A method will be presented to estimate the damping controller parameters systematically to obtain the desired performance using small signal stability analysis results. Furthermore, it will be shown that by strongly controlling the voltage of the point of common coupling, the damping of the oscillations produced by the sub-synchronous interaction between the wind power plant and the series compensated line can be improved. Based on the findings of this research, the thesis proposes a number of recommendations to be adopted when studying the sub-synchronous interactions in wind integrated power systems. These recommendations will facilitate to do such studies effectively and pinpoint the root cause of the sub-synchronous interactions.

Modeling of wind farms to determine their short circuit contribution in response to faults is a crucial part of system impact studies performed by power utilities. Short circuit calculations are necessary to determine protective relay settings, equipment ratings and to provide data for protection coordination. The plethora of different factors that influence the response of wind farms to short circuits makes short circuit modeling of wind farms an interesting, complex, and challenging task. Low voltage ride through (LVRT) requirements make it necessary for the latest generation of wind generators to be capable of providing reactive power support without disconnecting from the grid during and after voltage sags. If the wind generator must stay connected to the grid, a facility has to be provided to by-pass the high rotor current that occurs during voltage sags and prevent damage of the rotor side power electronic circuits. This is done through crowbar circuits which are of two types, namely active and passive crowbars, based on the power electronic device used in the crowbar triggering circuit. Power electronics-based converters and controls have become an integral part of wind generator systems like the Type 3 doubly fed induction generator based wind generators. The proprietary nature of the design of these power electronics makes it difficult to obtain the necessary information from the manufacturer to model them accurately. Also, the use of power electronic controllers has led to phenomena such as sub-synchronous control interactions (SSCI) in series compensated Type 3 wind farms which are characterized by non-fundamental frequency oscillations. SSCI affects fault current magnitude significantly and is a crucial factor that cannot be ignored while modeling series compensated Type 3 wind farms. These factors have led to disagreement and inconsistencies about which techniques are appropriate for short circuit modeling of wind farms. Fundamental frequency models like voltage behind transient reactance model are incapable of representing the majority of critical wind generator fault characteristics such as sub-synchronous interactions. The Detailed time domain models, though accurate, demand high levels of computation and modeling expertise. Voltage dependent current source modeling based on look up tables are not stand-alone models and provide only a black-box type of solution. The short circuit modeling methodology developed in this research work for representing a series compensated Type 3 wind farm is based on the generalized averaging theory, where the system variables are represented as time varying Fourier coefficients known as dynamic phasors. The modeling technique is also known as dynamic phasor modeling. The Type 3 wind generator has become the most popular type of wind generator, making it an ideal candidate for such a modeling method to be developed. The dynamic phasor model provides a generic model and achieves a middle ground between the conventional electromechanical models and the cumbersome electromagnetic time domain models. The essence of this scheme to model a periodically driven system, such as power converter circuits, is to retain only particular Fourier coefficients based on the behavior of interest of the system under study making it computationally efficient and inclusive of the required frequency components, even if non-fundamental in nature. The capability to model non-fundamental frequency components is critical for representing sub-synchronous interactions. A 450 MW Type 3 wind farm consisting of 150 generator units was modeled using the proposed approach. The method is shown to be highly accurate for representing faults at the point of interconnection of the wind farm to the grid for balanced and unbalanced faults as well as for non-fundamental frequency components present in fault currents during sub-synchronous interactions. Further, the model is shown to be accurate also for different degrees of transmission line compensation and different transformer configurations used in the test system.

The share of electricity generation in the power system being based on power electronics is increasing, which will impact the system in different ways, such as an increased risk for undesired interactions. An example is doubly fed induction generator (DFIG) based windfarms which have been shown to present negative resistance in (parts of) the sub-synchronous range (i.e., below the system frequency of 50 or 60 Hz). If such a wind farm is radially connected (deliberately or not) to a series compensated line, undamped or poorly damped sub-synchronous oscillations could occur due to sub-synchronous resonance. One possible cause of such interactions is related to the wind farm control system, and in such cases, the interaction between the wind farm and system leading to sub-synchronous oscillations is referred to as sub-synchronous control interaction (SSCI). This thesis aims to describe different types of so-called sub-synchronous oscillations, with a focus on SSCI. An investigation is performed to find out under what circumstances there is a risk of SSCI, and how one can evaluate this risk. Different methods of obtaining the impedance of non-linear systems (e.g., a wind farm) are discussed, with the method used in this thesis being a dynamic impedance scan. The dynamic impedance scan is implemented in PSCAD and uses a voltage (or current) perturbation of one frequency at a time and measures the current (or voltage) response at that frequency, subsequently giving the impedance as the voltage/current ratio. Combined with the impedance of the grid, screening studies were performed to identify the risk of SSCI under different conditions. A 200 MW photovoltaic (PV) farm is designed and implemented in PSCAD. The PV farm is connected to the same bus as a 200 MW DFIG wind farm, resulting in a hybrid wind and PV farm. The hybrid wind and PV farm is in turn connected to a series compensated transmission system made to resemble a typical Swedish system. Functionality is added to the PV farm that enables it to act as a static synchronous compensator (STATCOM) to damp sub-synchronous oscillations if needed. Simulations are performed in PSCAD showing that the PV farm is able to damp the sub-synchronous oscillations occurring when the wind farm is radially connected with the series compensated line due to a fault, thereby avoiding disconnection or damage to equipment. One of the main conclusions is that assessing the risk of SSCI (screening) is not an exact science, but a highly complex matter. This conclusion is drawn due to contradictory implications given when analysing the measured grid and wind farm impedances. For example, a series resonance point in the combined reactance (grid + wind farm) would suggest that there would be oscillations at this frequency during a fault, but this may not always be the case. The opposite also occurred, i.e., oscillations of a certain frequency occurred even though no series-resonance point was seen in the combined impedance. Nonetheless, the screening method did manage to identify risk cases based on a set of criteria listed in the thesis, although electromagnetic transient analysis (EMT) time-domain simulations should always be performed for verification. The other main conclusion is that a PV farm installed at the point of common coupling (PCC) of a wind farm, i.e., a hybrid wind and PV farm, is able to damp sub-synchronous oscillations by acting as a PV-STATCOM. The use of combined assets, such as utilizing a PV farm to counteract SSCI in a wind farm, means that additional investments, for example in the form of a STATCOM, for this purpose could be avoided.

The electric power system is designed to economically and reliably transmit electricity to homes, industry, and businesses. The economic impact of the electric grid was demonstrated by the 2003 blackout's visible impact in the graph of the yearly gross domestic product of the Unites States. However, because the number of customers is so large and economies of scale are leveraged to keep electricity prices low, utilities are strongly interconnected. Performing comprehensive engineering analyses to ensure reliable operation is still impossible. Instead, heuristics and safety factors are incorporated into planning processes to continually meet demand in a way that complies with Federal regulations. As evidenced by the infrequency of blackouts in the United States, the sophisticated planning processes have up to date been relatively successful. However, the power system is constantly changing. Electrical generators based on renewable energies are a beneficial addition to the grid, but these and other technological changes like high-voltage power electronic converters also come with their own challenges. These systems as currently employed tend to have a different impact on the reliability of operation than traditional fossil fuel based generators. As the system changes, so do the engineering analyses required to ensure reliable operation. In particular, the wind energy conversion systems (WECS) negatively impact the response of the grid to disturbances in certain ways due to inherent challenges harnessing the wind as an energy sources. These negative impacts (and the advent of powerful personal computing) require an increase in the sophistication of power system models. Thus, there are competing challenges: the scale of the power system necessitates computationally efficient modeling, but the complexity of analysis required to maintain reliable operation is also increasing. The primary aim of this study is to develop models and methods for more detailed yet computationally manageable simulation. To this aim, higher order linearizations and the properties of linear systems (graph theory and linear algebra) are exploited. More specifically, this document contains three studies. In the short term planning and situational awareness context, a method is proposed to quickly check credible outages of important grid equipment. This methodology enables the inspection of a wider breadth of system conditions to ameliorate the negative impacts of the unpredictability of the wind. A linear model in the traditional sense is also developed to model any arbitrary number of wind turbines in a wind farm. This enables industry players to study the impacts wind turbine interaction on the dynamic stability of the grid in response to small disturbances. Finally, a wind farm is modeled as a large matrix to model even nonlinear behavior of wind farms. This helps industry players analyze the impact of large disturbances on the grid. / Doctor of Philosophy / The electric power system is designed to economically and reliably transmit electricity to homes, industry, and businesses. The economic impact of the electric grid was demonstrated by the 2003 blackout’s visible impact in the graph of the yearly gross domestic product of the United States. However, because the number of customers is so large and economies of scale are leveraged to keep electricity prices low, utilities are strongly interconnected. Performing comprehensive engineering analyses to ensure reliable operation is still impossible. Instead, heuristics and safety factors are incorporated into planning processes to continually meet demand in a way that complies with Federal regulations. As evidenced by the infrequency of blackouts in the United States, the sophisticated planning processes have up to date been relatively successful. However, the power system is constantly changing. Electrical generators based on renewable energies are a beneficial addition to the grid, but these and other technological changes like high-voltage power electronic converters also come with their own challenges. These systems as currently employed tend to have a different impact on the reliability of operation than traditional fossil fuel based generators. As the system changes, so do the engineering analyses required to ensure reliable operation. In particular, the wind energy conversion systems (WECS) negatively impact the response of the grid to disturbances in certain ways due to inherent challenges harnessing the wind as an energy sources. These negative impacts (and the advent of powerful personal computing) require an increase in the sophistication of power system models. Thus, there are competing challenges: the scale of the power system necessitates computationally efficient modeling, but the complexity of analysis required to maintain reliable operation is also increasing. The primary aim of this study is to develop models and methods for more detailed yet computationally manageable simulation. To this aim, higher order linearizations and the properties of linear systems (graph theory and linear algebra) are exploited. More specifically, this document contains three studies. In the short term planning and situational awareness context, a method is proposed to quickly check credible outages of important grid equipment. This methodology enables the inspection of a wider breadth of system conditions to ameliorate the negative impacts of the unpredictability of the wind. A linear model in the traditional sense is also developed to model any arbitrary number of wind turbines in a wind farm. This enables industry players to study the impacts wind turbine interaction on the dynamic stability of the grid in response to small disturbances. Finally, a wind farm is modeled as a large matrix to model even nonlinear behavior of wind farms. This helps industry players analyze the impact of large disturbances on the grid.

Recently, with growing application of wind power, the system based on the doubly fedinduction generator (DFIG) has become the one of the most popular concepts. Theproblem of connecting to the grid is also gradually revealed. As an effective solution toconnect offshore wind farm, VSC-HVDC line is the most suitable choice for stabilityreasons. However, there are possibilities that the converter of a VSC-HVDC link canadversely interact with the wind turbine and generate poorly damped sub-synchronousoscillations. Therefore, this master thesis will derive the linear model of a single DFIG aswell as the linear model of several DFIGs connecting to a VSC-HVDC link. For thelinearization method, the Jacobian transfer matrix modeling method will be explainedand adopted. The frequency response and time-domain response comparison betweenthe linear model and the identical system in PSCAD will be presented for validation. / Nyligen, med ökande tillämpning av vindkraft, det system som bygger på den dubbeltmatad induktion generator (DFIG) har blivit en av de mest populära begrepp. Problemetmed att ansluta till nätet är också gradvis avslöjas. Som en effektiv lösning för att anslutavindkraftpark är VSC -HVDC linje det lämpligaste valet av stabilitetsskäl. Det finns dockmöjligheter att omvandlaren en VSC-HVDC länk negativt kan interagera medvindturbinen och genererar dåligt dämpade under synkron svängningar. Därför kommerdetta examensarbete härleda den linjära modellen av en enda DFIG liksom den linjäramodellen av flera DFIGs ansluter till en VSC-HVDC -länk. För arise metoden kommerJacobian transfer matrix modelleringsmetodförklaras och antas. Jämförelse mellan denlinjära modellen och identiskt system i PSCAD frekvensgången och tidsdomänensvarkommer att presenteras för godkännande.

The power converter is one of the key components in power system applications such as high voltage direct current (HVDC) systems and the grid connection of intermittent sources such as wind and solar power. However, the increased penetration of converter-based generation introduces challenges, such as sub-synchronous interaction between the converter control system and the grid. These control interactions are characterized by fast-growing, subsynchronous oscillations (SSO). This thesis deals with the analysis of sub-synchronous control interactions (SSCI) between doubly-fed induction generator (DFIG)-based wind farms and series compensated transmission lines. Moreover, the thesis aims to identify a method for mitigating the sub-synchronous oscillations using a static synchronous compensator (STATCOM), with a supplementary damping controller. The study is based on work in PSCAD/EMTDC and uses a system based on the IEEE first benchmark model, acting as a grid, and the scaled power output of a DFIG turbine model, modeling a wind farm. Initial impedance-based analysis in the frequency domain shows that the DFIG wind farm has a negative resistance throughout the sub-synchronous frequency range. A negative resistance may result in negative damping of the system and further introduce the risk of instability. The wind farm resistance and, in turn, system stability is affected by the current control loop of the DFIG-converter. The transmission line compensation factor largely impacts the system stability, while the power output has a minor effect. A time-domain analysis is performed to verify the result of the frequency domain analysis. Further on, a grid-forming STATCOM is added to the system for VAr compensation. Additional stability analysis shows that even though improvingthe stability, the STATCOM alone is not adequate to mitigate the SSCI. The proposed damping strategy is based on modifying the STATCOM voltage reference andcan be divided into three steps: detecting the SSO, estimating the sub-synchronous component, and modifying the extracted signal. The detection algorithm is based on a half-cycle comparator, while the modification is done through a proportional gain. When estimating the sub-synchronous components, two methods are proposed and compared. The first estimation method is based on a conventional power system stabilizer (PSS) method, and the second is afilter-less method.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T11:06:45Z No. of bitstreams: 1 rodrigovianello.pdf: 847018 bytes, checksum: 7ad17011832e8156b0fa361091a1375a (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-12-22T12:53:13Z (GMT) No. of bitstreams: 1 rodrigovianello.pdf: 847018 bytes, checksum: 7ad17011832e8156b0fa361091a1375a (MD5) / Made available in DSpace on 2016-12-22T12:53:13Z (GMT). No. of bitstreams: 1 rodrigovianello.pdf: 847018 bytes, checksum: 7ad17011832e8156b0fa361091a1375a (MD5) Previous issue date: 2010-02-24 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho apresenta a proposição de duas metodologias inovadoras no campo da estimação fasorial. A primeira delas propõe a estimação do fasor da componente fundamental na presença de harmônicos e decaimento CC exponencial e é baseada na aplicação de filtros DFT (Discrete Fourier Transform) e de alguns métodos de processamento de sinais, tais como janelamento, modulação e DTFT (Discrete Time Fourier Transform). A segunda metodologia também propõe a estimação do fasor da componente fundamental, mas em um cenário mais complexo onde estão presentes no sinal, além dos harmônicos e decaimento CC exponencial, as oscilações subsíncronas. Esta metodologia é baseada na aplicação de redes neurais artificiais e de alguns métodos de processamento de sinais. Ambas as metodologias foram avaliadas frente a métodos tradicionais de estimação fasorial e apresentaram desempenhos superiores na presença de ruídos. / Thisthesispresents thepropositionoftwonovelmethodsin thefieldofphasor estimation. The first proposes to estimate the phasor of the fundamental component in the presence of harmonicsandexponentialdecayingDC.ThismethodologyisbasedontheapplicationoffiltersDFT (Discrete Fourier Transform) and some methods of signal processing such as windowing, modulation and DTFT (Discrete Time Fourier Transform). The second approach also proposes to estimate the phasor of the fundamental component, but in a more complex scenario formed for harmonics, exponential decaying DC and the sub-synchronous oscillations . This methodology isbasedontheapplicationofartificialneuralnetworksandsomemethodsofsignalprocessing. Both methods were evaluated against traditional methods of phasor estimation and the simulations showed that the two proposed methods were more accurate then others in presence of noise.

Wind farms are commonly connected to the main grid through compensated lines which increases the power transfer capability of the line. Double Fed Induction Generator (DFIG) wind turbines in connection to compensated lines can experience Sub-Synchronous Control Interaction (SSCI) which can bring system quantities above allowed levels. The work conducted in this thesis describes the use of harmonic injection to analyze the DFIG. The method describes how to analyze the DFIG such that it can be used to determine if the DFIG will experience SSCI. By using Electro-Magnetic Transient (EMT) software, the work shows how the method can be used to analyze the DFIG both to find the resonant frequency as well as if the oscillations will be sufficiently damped or undamped. Using the method of harmonic injection, the DFIG’s internal control parameters are also investigated and the equivalent frequency dependant resistance of the system is measured. After analyzing the DFIG, a Power Oscillation Damper (POD) is implemented as a supplementary control system in the DFIG control system to dampen the SSCI. The POD is optimized using PSCAD and is validated using the harmonic injection method. / Vindkraftverk är vanligtvis anslutna till stamnätet genom kompenserade ledningar, vilket ökar ledningens effektöverföringsfaktor. Dubbelmatade induktionsgeneratorer (DFIG) i anslutning med kompenserade ledningar kan uppleva subsynkrona kontrollinteraktioner (SSCI) som kan leda till att vissa systemstorheter överskrider tillåtna nivåer. Det arbete som utförs i denna rapport beskriver användningen av harmonisk injektion för att analysera DFIG. Metoden beskriver hur man analyserar DFIG så att den kan användas för att avgöra om DFIG kommer att uppleva SSCI. Genom att använda EMT-programvara (Electro-Magnetic Transient) visar arbetet i rapporten hur metoden kan användas för att analysera DFIG både för att hitta resonansfrekvensen och för att avgöra om svängningarna kommer att vara tillräckligt dämpade eller odämpade. Med hjälp av metoden för harmonisk injektion undersöks också DFIG:s interna styrparametrar och systemets ekvivalenta frekvensberoende motstånd mäts. Efter analys av DFIG:en implementeras en dämptillsats (POD) som ett kompletterande styrsystem i DFIG:s styrsystem för att dämpa SSCI. POD optimeras med hjälp av PSCAD och valideras med hjälp av harmonisk injektionsmetod.

Series compensation is extensively applied to the transmission lines to increase the power transfer capability of transmission lines, reduce transmission losses, improve voltage profiles, and improve power oscillation damping and transient stability of power systems. But it modifies the apparent impedance of the transmission lines during fault conditions and might cause the distance protection of transmission lines to encounter directional discrimination issues and reach problems. The non-linear characteristic of metal oxide varistor in series compensation model creates further complexity to the fault analysis and might affects the performance of conventional distance protection scheme. The distance protection issues in the series compensated lines need to be addressed for the reliable and sustainable operation of power system.The directional discrimination issues related to current inversion and voltage inversion phenomenon, and reach problems related to sub-synchronous oscillation phenomenon are addressed in this thesis report. This report aims to analyse the impacts of series compensation on the performance of conventional distance relays, and proposes a new protection solution to mitigate the shortcomings of distance relays in the series compensated lines. The proposed new protection solution includes: new tripping characteristic of quadrilateral distance relays to cope with the steady-state reach problems due to current or voltage inversion, and a new high-pass filtering technique to handle the transient reach problems due to SSO.The proposed new protection algorithm is developed in MATLAB. The performance of new protection algorithm is evaluated by simulating a 500 kV two-source power system with a 200 km series compensated line in EMTDC/ PSCAD (Manitoba Hydro). The proposed new protection solution is found to be beneficial. / Seriekompensation tillämpas i stor utsträckning på överföringsledningarna för att öka överföringsförmågan hos överföringsledningar, minska överföringsförluster, förbättra spänningsprofiler och förbättra effektdämpning och övergående stabilitet hos elsystem. Men det ändrar transmissionslinjernas uppenbara impedans under felförhållanden och kan orsaka att distansskydd för överföringsledningarna stöter på diskrimineringsproblem och uppnår problem. Den icke-linjära egenskapen hos metalloxidvaristor i seriekompensationsmodell skapar ytterligare komplexitet för felanalysen och kan påverka prestandan hos konventionella distansskyddssystem. Distansskydd problemen i seriekompenserade linjer måste lösas för en pålitlig och hållbar drift av elsystemet. De riktningsdiskrimineringsproblem som är relaterade till det aktuella inversions- och spänningsinversionsfenomenet och uppnår problem relaterade till subsynkron oscillationsfenomen tas upp i denna avhandlingsrapport. Denna rapport syftar till att analysera effekterna av seriekompensation för prestanda hos konventionella distansreläer och föreslår en ny skyddslösning för att mildra bristerna i distansreläerna i seriekompenserade linjer. Den föreslagna nya skyddslösningen innefattar: Ny utlösningskaraktäristik för fyrsidig distansreläer för att klara avståndet med stillastående / räckvidden på grund av ström- eller spänningsinversion och en ny högpassfiltreringsteknik för hantering av övergående över- Nå problem på grund av SSO. Den föreslagna nya skyddsalgoritmen har utvecklats i MATLAB. Utförandet av den nya skyddsalgoritmen utvärderas genom simulering av ett 500 kV två-källa kraftverk med en 200 km serie kompenserad linje i EMTDC / PSCAD (Manitoba Hydro). Den föreslagna nya skyddslösningen har visat sig vara fördelaktig.