Power systems are extremely non-linear systems which require substantial modeling and control efforts to run continuously. The movement of the power system in parameter and state space is often not well understood, thus making it difficult or impossible to determine whether the system is nearing instability. This dissertation demonstrates several ways in which the power system stability boundary can be calculated. The power system movements evaluated here address the effects of inter-area oscillations on the system which occur in the seconds to minutes time period. The first uses gain scheduling techniques through creation of a set of linear parameter varying (LPV) systems for many operating points of the non-linear system. In the case presented, load and line reactance are used as parameters. The scheduling variables are the power flows in tie lines of the system due to the useful information they provide about the power system state in addition to being available for measurement. A linear controller is developed for the LPV model using H₂/H∞ with pole placement objectives. When the control is applied to the non-linear system, the proposed algorithm predicts the response of the non-linear system to the control by determining if the current system state is located within the domain of attraction of the equilibrium. If the stability domain contains a convex combination of the two points, the control will aid the system in moving towards the equilibrium. The second contribution of this thesis is through the development and implementation of a pseudo non-linear evaluation of a power system as it moves through state space. A system linearization occurs first to compute a multi-objective state space controller. For each contingency definition, many variations of the power system example are created and assigned to the particular contingency class. The powerflow variations and contingency controls are combined to run sets of time series analysis in which the Lyapunov function is tracked over three time steps. This data is utilized for a classification analysis which identifies and classifies the data by the contingency type. The goal is that whenever a new event occurs on the system, real time data can be fed into the trained tree to provide a control for application to increase system damping. / Ph. D. / The goal of the utility, reliability coordinators, academics, and regulators is to keep the lights on. The contributions presented in this dissertation aims to provide a methodology and algorithm with which that goal can be met. Although the power system requires the balancing of many different components, it can be boiled down to ensuring equilibrium between load served and generation provided. Because the utility goal is to keep the lights on – and thus not change the load of the customers by turning their lights off, the utility only has control over the generation side of this equation. A see-saw can be used to imagine this balance, but it will also require a feedback loop to ensure that generation will increase or decrease as the load changes. Another way to visualize the power system is to imagine a marble at the bottom of a bowl. If the marble is perturbed too much, it will fly out of the bowl and become what is called unstable. However, if the marble is nudged lightly, it will return back to its resting place at the bottom of the ball – which could be considered a stable equilibrium. A possible control for this type of system would tilt the bowl with a feedback signal based on the location or speed of the marble as it moved around the inside of the bowl. By providing a feedback control, the strength with which the marble can be hit can increase beyond if the bowl were to remain stagnant. However, if the marble is hit very hard, it will not matter if there is feedback control, the marble will veer out of the bowl into instability. This example serves as an analogy for the power system where the current operating point of the power system is the marble and the stable areas of operation are represented by the bowl. The feedback control for the work explored here utilizes information about the generator states to feedback to HVDC lines to strengthen the system. The power system modeling and control design involved in this dissertation aims to determine how much the power system can be perturbed before reaching the edge of the “bowl.”

Multi-pulse transformer/rectifier systems are becoming increasingly popular in power distribution systems. These topologies can be found in aircraft power systems, motor drives, and other applications that require low total harmonic distortion (THD) of the input line current. This increase in the use of multi-pulse transformer topologies has led to the need to study large systems composed of said units and their interactions within the system. There is also an interest in developing small-signal models so that stability issues can be studied. This thesis presents a procedure for the average model of multi-pulse transformer/rectifier topologies. The dq rotating reference frame was used to develop the average model and parameter estimation is incorporated through the use of polynomial fits. The average model is composed of nonlinear dependent sources and linear passive components. A direct benefit from this approach is a reduction in simulation time by two orders of magnitude. The average model concept demonstrates that it accurately predicts the dynamics of the system being studied. In particular, two specific topologies are studied, the 12-pulse hexagon transformer/rectifier (hex t/r) and the 18-pulse autotransformer rectifier unit (ATRU). In both cases, detailed switching model results are used to verify the operation of the average model. In the case of the hex t/r, the average model is further validated with experimental data from an 11 kVA prototype. The hex t/r output impedance, obtained from the linearized average model, has also been verified experimentally. / Master of Science

The unconventional improvements in the power electronics field have been the primary reason for massive deployment of renewable energy sources in the electrical power grid over the past several decades. This needed trend, together with the increasing penetration of micro-, and nano- grids, is bringing significant improvements in system controllability, performance, and energy availability, but is fundamentally changing the nature of electronically-interfaced sources and loads, altering their conventionally mild aggregate dynamics, and inflicting low- and high- frequency dynamic interactions that never before existed at this magnitude. This problem is not restricted only to the grid; modern electronic power distribution systems built for airplanes, ships, electric vehicles, data-centers, and homes, comprise dozens, even hundreds of power electronics converters, produced by different manufacturers, who provide very limited details on converters' dynamic behavior - distinctiveness that has the highest impact on how two converters, or converter and a system interact. Consequently, substantial dispersion of power electronics into the future grid will significantly depend on engineers' capability to understand how to model and dynamically control power flow and subsystem interactions. It is therefore essential to continue developing innovative methods that allow easier system-level modeling, continuous monitoring of dynamic interactions, and advanced control concepts of power electronics converters and systems. The dissertation will start with a "black box" approach to modeling of three-phase power electronics converters, introducing a method to remove source and load dynamics from in-situ measured terminated frequency responses. It will be then shown how converter, itself, can perform an online stability assessment knowing its own unterminated dynamics, and being able to measure all terminal immittances. The dissertation will further advance into an approach to control power electronics converters based on the electro-mechanical duality with synchronous machines, and end with selected examples of system-level operation, where small-signal instability in multi-source power systems can be mitigated using this concept. / Ph. D. / The modern technological advancements and ever-increasing needs for a sustainable future silently demand a serious revision of the conventional practice in electricity production, distribution, and utilization. These technologies are already challenging the limits of the biggest and most complex system ever built by humankind - the electrical grid. One practical solution to this problem is much higher dispersion of electronic power conversion systems capable of decoupling dynamics between system sources, distribution, and loads, while improving system controllability, reliability, and efficiency. Such a trend is already happening, and there has been an increased immersion of power electronics converters in electric cars, ships, airplanes, and the grid, in an effort to replace their traditional thermal, mechanical, hydraulic, and pneumatic systems. The goals have been to reduce the size, weight, and operational costs while increasing efficiency and reliability. In all these applications, a majority of energy sources and loads are interfaced to the power system through power electronics converters ranging in power from few watts to hundreds of megawatts. However, massive dispersion of power electronics into the future grid will significantly depend on engineers’ capability to understand how to model and dynamically control power flow and subsystem interactions. It is important to continue researching innovative methods that allow easier system-level modeling, continuous monitoring of interactions, and advanced control concepts of power electronics converters and systems. This dissertation hence addresses modeling of power electronics converters using their behavioral models, and shows how these models can assist the stability assessment of the system converters operate in. Additionally, dissertation presents an alternative way to control power electronics converters to behave as synchronous machines, and how this concept can be used to mitigate some stability problems.

Modular multilevel converter type voltage source converter (MMC-VSC) is a potential candidate for present and future HVdc projects. The d-q decoupled control system is widely used to control MMC-VSC systems. Selection of PI-controller parameters for MMC-VSC systems is a challenging task as control loops are not completely decoupled. Since there is no widely accepted method to tune these control loops, the industry practice is to use the trial and error approach that requires a great amount of time. Therefore, it is required to develop a systematic procedure to tune PI-controllers considering necessary system dynamics and also to propose guidelines for control system design. This thesis introduces a systematic procedure to determine PI-controller parameters for the d-q decoupled control system. A linearized state-space model of an MMC-VSC system is developed to calculate the frequency-domain attributes. The control tuning problem is formulated as an optimization problem which is general and any meta-heuristic method can be used to solve the problem. In this thesis, the simulated annealing is applied to solve the problem. The efficacy of the tuned parameters is tested on the electromagnetic transient model of the test system on the real-time digital simulators (RTDS). In addition, it is shown that the proposed method is suitable to tune PI-controller parameters for MMC-VSC systems connected to strong as well as weak ac networks. Further, this thesis investigates the effects of d-q decoupled controller parameters, phase-locked loop (PLL) gains, and measuring delays on the stability and performance of the MMC-VSC test system. It is shown that the converter controllers have greater influence on the system stability and the impact of PLL gains is negligible unless very high PLL gains are used. In addition, the negative impact of measuring delays in instantaneous currents and voltages is also analysed by performing eigenvalue and sensitivity analysis. Finally, a set of guidelines for control design of MMC-VSC systems is summarized. In general, the proposed control tuning procedure would be useful for the industry to tune PI-controllers of MMC-VSC systems. Furthermore, the proposed methodology is generic and can be adapted to tune of any dynamic device in power systems. / February 2017

This dissertation is focused on the research efforts to develop the growth, processing, and modeling technologies for GaN-based Heterojunction Field Effect Transistors (HFETs). The interest in investigating GaN HFETs is motivated by the advantageous material properties of nitride semiconductor such as large band gap, large breakdown voltage, and high saturation velocity, which make it very promising for the high power and microwave applications. Although enormous progress has been made on GaN transistors in the past decades, the technologies for nitride transistors are still not mature, especially concerning the reliability and stability of the device. In order to improve the device performance, we first optimized the growth and fabrication procedures for the conventional AlGaN barrier HFET, on which high carrier mobility and sheet density were achieved. Second, the AlInN barrier HFET was successfully processed, with which we obtained improved I-V characteristics compared with conventional structure. The lattice-matched AlInN barrier is beneficial in the removal of strain, which leads to better carrier transport characteristics. Furthermore, new device structures have been examined, including recess-gate HFET with n+ GaN cap layer and gate-on-insulator HFET, among which the insertion of gate dielectrics helps to leverage both DC and microwave performances. In order to depict the microwave behavior of the HFET, small signal modeling approaches were used to extract the extrinsic and intrinsic parameters of the device. An 18-element equivalent circuit model for GaN HFET has been proposed, from which various extraction methods have been tested. Combining the advantages from the cold-FET measurements and hot-FET optimizations, a hybrid extraction method has been developed, in which the parasitic capacitances were attained from the cold pinch-off measurements while the rest of the parameters from the optimization routine. Small simulation error can be achieved by this method over various bias conditions, demonstrating its capability for the circuit level design applications for GaN HFET. Device physics modeling, on the other hand, can help us to reveal the underlying physics for the device to operate. With the development of quantum drift-diffusion modeling, the self-consistent solution to the Schrödinger-Poisson equations and carrier transport equations were fulfilled. Lots of useful information such as band diagram, potential profile, and carrier distribution can be retrieved. The calculated results were validated with experiments, especially on the AlInN layer structures after considering the influence from the parasitic Ga-rich layer on top of the spacer. Two dimensional cross-section simulation shows that the peak of electrical field locates at the gate edge towards the drain, and of different kinds of structures the device with gate field-plate was found to efficiently reduce the possibility of breakdown failure.

The primary goal of this research is to put into code a unique approach to addressing problems apparent with nonlinear FET models which were exposed by Calvo in her work in 1994. Since that time, the simulation software for which her model was appropriate underwent a significant update, necessitating the rewriting of her model code for a few applicable FET models in a Verilog-A, making it more compatible with the new versions of software and simulators. The problems addressed are the inconsistencies between the small-signal model and the corresponding large-signal models due to a factor called transcapacitance. It has been noted by several researchers that the presence of a nonlinear capacitor in a circuit model mathematically implies the existence of a parallel transcapacitor, if the value of its capacitance is a function of two bias voltages, the local and a remote voltage. As a consequence, simulating small signal excursions using the linear model, if the latter does not include the transcapacitance, which is inevitably present. The Calvo model attempted to improve the performance of these models by modifying terms in the charge source equations which minimize these transcapacities. Thanks to the present effort, Calvo's theory is now incorporated in the Angelov Model and can also be implemented in some other popular existing models such as Curtic, Statz and Parker Skellern models.

In this thesis a buck converter has been developed to be used as a test bench in power electronics laboratory. For this purpose, first, steady-state and small-signal analyses of a buck converter is carried out, then open-loop and closed-loop control of the converter are developed and simulated. Then, the circuit is manufactured and tested. The test results are compared with the simulation results. Finally, an experimantal procedure is prepared to enable the students to perform the experiment in the laboratory with the test bench developed.

In this thesis a boost converter is developed to be used as a test bench in power electronics laboratory. For this purpose, first, steady-state and small-signal analyses of a boost converter are carried out, then closed loop control of the converter is developed and simulated. Then, the circuit is designed and manufactured. The test results are compared with the simulation results. Finally, an experimantal procedure is prepared to enable the students to perform the experiment in the laboratory with the test bench developed.

This thesis presents an investigation into the power transmission limitations imposed on a VSC-HVdc converter by ac system strength and ac system impedance characteristics, quantified by the short circuit ratio (SCR). An important result of this study is that the operation of the converter is not only affected by the SCR’s magnitude, but is also significantly affected by the ac system’s impedance angle at the fundamental frequency. As the ac impedance becomes more resistive, the minimum SCR required at the rectifier side increases from that required for ideally inductive ac impedance, but it decreases at the inverter side. The finite megavolt ampere (MVA) limit of the VSC imposes a further limitation on power transfer, requiring an increase in the value of the minimum SCR. This limitation can be mitigated if additional reactive power support is provided at the point-common-connection. A state-space VSC model was developed and validated with a fully detailed non-linear EMT model. The model showed that gains of the phased-locked-loop (PLL), particularly at low SCRs greatly affect the operation of the VSC-HVdc converter and that operation at low SCRs below about 1.6 is difficult. The model also shows that the theoretically calculated power-voltage stability limit is not attainable in practice, but can be approached if the PLL gains are reduced. The thesis shows that as the VSC-HVdc converter is subject to large signal excitation, a good controller design cannot rely on small signal analysis alone. The thesis therefore proposes the application of optimization tools to coordinate the controls of multiple converters in a dc grid. A new method, the "single converter relaxation method", is proposed and validated. The design procedure of control gains selection using the single converter relaxation method for a multi-converter system is developed. A new method for selecting robust control gains to permit operation over a range of operation conditions is presented. The coordination and interaction of control parameters of multi-terminal VSC are discussed. Using the SCR information at converter bus, the gain scheduling approach to optimal gains is possible. However, compared to robust control gains setting, this approach is more susceptible to system instability.

This thesis describes the development of several small signal analysis methods for the modelling of power electronic converters. The methods are written generally and are intended to be able to be applied to all converter classes. In the penultimate chapter these general models are used to model the capacitor commutated converter. All the contained methods are based around a time domain small signal model. This time domain small model is a linearization of a power electronic system of passive components and ideal switches described as a hybrid system. The key problem in the derivation of the small signal model is the correct determination and description of the linearized effect of switching instant variation. Three analysis methods based upon the small signal model are advanced in this thesis, these are; time domain sensitivity matrices for use in a Newton determination of the cyclic steady state of a power electronic converter, partial waveform construction of harmonic sensitivity matrices for studying sensitivity of converters to harmonic disturbances, and harmonic state space models also for the construction of harmonic sensitivity matrices and for study of dynamic systems. Each modelling technique is applied to the more common converter topologies of the Buck-Boost converter and the Graetz Bridge before being finally applied to the capacitor commutated converter. Each technique is compared to PSCAD-EMTDC simulations for verification.