This thesis presents a new general purpose power system simulation technique based on dynamic phasors and conventional power system simulation methods. The method developed in this work converts time-domain circuits to equivalent dynamic phasor representations. These dynamic phasor equivalents are then simulated using nodal analysis and numerical integrator substitution. Simple linear circuit models are presented first in order to demonstrate that the new method is capable of accurately simulating small systems. The method developed in this work is then expanded to include control systems, power electronic converters, and synchronous machines. Visual comparisons with simulation results obtained using time-domain electromagnetic transient simulators demonstrate that the new dynamic phasor-based technique is capable of accurately simulating power system components.

This thesis develops the dynamic phasor model of a line-commutated converter (LCC) high-voltage direct current (HVDC) transmission system. The mathematical definition and properties of dynamic phasors are utilized to model both the dc-side and the ac-side of a LCC-HVDC transmission system as well as 6-pulse Graetz bridge, which is the building block of such a system. The developed model includes low-frequency dynamics of the systems, i.e., fundamental frequency component (50 Hz) at the ac-side and dc component at the dc-side, and removes high-frequency transients. The developed model, however, is capable of accommodating higher harmonics if necessary. The model is also able to simulate the system during abnormal modes of operations such as unbalanced operation and commutation failure. In order to develop the dynamic phasor model of a line-commutated converter, the concept of switching functions is utilized. The developed model is capable of capturing large-signal transients of the system as well as steady state operating conditions. The model can be used in order to decrease the computational intensity of LCC-HVDC simulations. The developed model in this thesis enables the user to consider each harmonic component individually; this selective view of the components of the system response is not possible to achieve in conventional electromagnetic transient simulations. / October 2016

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.

abstract: An increase in the number of inverter-interfaced photovoltaic (PV) generators on existing distribution feeders affects the design, operation, and control of the distri- bution systems. Existing distribution system analysis tools are capable of supporting only snapshot and quasi-static analyses. Capturing the dynamic effects of the PV generators during the variation in the distribution system states is necessary when studying the effects of controller bandwidths, multiple voltage correction devices, and anti-islanding. This work explores the use of dynamic phasors and differential algebraic equations (DAE) for impact analysis of the PV generators on the existing distribution feeders. The voltage unbalance induced by PV generators can aggravate the existing unbalance due to load mismatch. An increased phase unbalance significantly adds to the neutral currents, excessive neutral to ground voltages and violate the standards for unbalance factor. The objective of this study is to analyze and quantify the impacts of unbalanced PV installations on a distribution feeder. Additionally, a power electronic converter solution is proposed to mitigate the identified impacts and validate the solution's effectiveness through detailed simulations in OpenDSS. The benefits associated with the use of energy storage systems for electric- utility-related applications are also studied. This research provides a generalized framework for strategic deployment of a lithium-ion based energy storage system to increase their benefits in a distribution feeder. A significant amount of work has been performed for a detailed characterization of the life cycle costs of an energy storage system. The objectives include - reduction of the substation transformer losses, reduction of the life cycle cost for an energy storage system, and accommodate the PV variability. The distribution feeder laterals in the distribution feeder with relatively high PV generation as compared to the load can be operated as microgrids to achieve reliability, power quality and economic benefits. However, the renewable resources are intermittent and stochastic in nature. A novel approach for sizing and scheduling the energy storage system and microtrubine is proposed for reliable operation of microgrids. The size and schedule of the energy storage system and microturbine are determined using Benders' decomposition, considering the PV generation as a stochastic resource. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers. The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics. Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions. The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions. The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good. Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments. / QC 20100628

[pt] O incremento de geração fotovoltaica de grande porte traz consideráveis mudanças nas características operativas e dinâmicas do sistema quando este é submetido a grandes distúrbios. Um dos problemas técnicos mais relevantes é a estabilidade transitória, já que a geração intermitente ligada ao sistema por conversores eletrônicos não contribui para o aumento da inércia total do sistema. Entretanto, os conversores eletrônicos podem, potencialmente, trazer novas oportunidades de controle rápido para dar suporte aos geradores síncronos em resposta a um distúrbio severo. No presente trabalho propõe uma estratégia de controle para inversores fotovoltaicos baseado na injeção da corrente com um grande impacto na resposta transitória do ângulo do rotor da máquina síncrona, identificada através da análise de sensibilidade dos autovalores e dos fatores de participação. Ao fazer isso, é possível aumentar a potência ativa da máquina síncrona próximo do seu valor pré-falta, reduzindo o desequilíbrio entre o torque elétrico e mecânico. A estratégia de controle proposta foi testada experimentalmente, utilizando um inversor e uma montagem máquina síncrona-motor e, através da simulação de um sistema híbrido com um sistema fotovoltaico de grande porte. Os resultados mostram que a estratégia de controle proposta não está apenas em conformidade com os requisitos dos código da rede para melhorar a estabilidade da tensão durante uma perturbação grave, mas também é capaz de manter a estabilidade transitória da rede provando, assim, ser uma melhor alternativa em relação à capacidade FRT requerida pelos códigos de rede. / [en] The increase in photovoltaic generation has caused changes in the power system s operative and dynamic characteristics when subjected to severe disturbances. One of the most relevant problems associated with this renewable energy source is the transient stability, as renewable generation connected to the system by electronic converters does not contrinute to the increase of the total inertia of the system. However, electronic converters can potentially bring new opportunities for rapid control to support synchronous generators in response to severe disturbance. The present work proposes a control strategy for photovoltaic inverters based on the injection of the current with a major impact on the transient response of the synchronous machine rotor angle, identified through the eigenvalue sensitivity analysis and the participation factors. By doing so, it is possible to increase the synchronous machine active power output close to its pre-fault value, reducing the disequilibrium between mechanical and electrical torque. The proposed control strategy was experimentally tested using an inverter and a synchronous-motor machine assembly and, by simulating a hybrid system with a large photovoltaic system. The results show that the proposed control strategy not only conforms to the grid codes requirements to improve voltage stability during a severe disturbance, but is also able to maintain transient stability thus proving to be a better alternative to the FRT capability required by the grid codes.