STATE OF CHARGE BASED DROOP SURFACE FOR OPTIMAL CONTROL OF DC MICROGRIDS

For a microgrid with a high penetration level of renewable energy, energy storage use becomes more integral to the system performance due to the stochastic nature of most renewable energy sources. This thesis examines the use of droop control of an energy storage source in dc microgrids in order to optimize a global cost function. The approach involves using a multidimensional surface to determine the optimal droop parameters based on load and state of charge. The optimal surface is determined using knowledge of the system architecture and can be implemented with fully decentralized source controllers. The optimal surface control of the system is presented. Derivations of a cost function along with the implementation of the optimal control are included. Results were verified using a hardware-in-the-loop system.

Optical Waveguides and Structures for Short Haul Optical Communication Channels within Printed Circuit Boards

Optical waveguides have shown promising results for use within printed circuit boards. These optical waveguides have higher bandwidth than traditional copper transmission systems and are immune to electromagnetic interference. Design parameters for these optical waveguides are needed to ensure an optimal link budget. Modeling and simulation methods are used to determine the optimal design parameters needed in designing the waveguides. As a result, optical structures necessary for incorporating optical waveguides into printed circuit boards are designed and optimized. Embedded siloxane polymer waveguides are investigated for their use in optical printed circuit boards. This material was chosen because it has low absorption, high temperature stability, and can be deposited using common processing techniques. Two sizes of waveguides are investigated, 50 $unit{mu m}$ multimode and 4 - 9 $unit{mu m}$ single mode waveguides. A beam propagation method is developed for simulating the multimode and single mode waveguide parameters. The attenuation of simulated multimode waveguides are able to match the attenuation of fabricated waveguides with a root mean square error of 0.192 dB. Using the same process as the multimode waveguides, parameters needed to ensure a low link loss are found for single mode waveguides including maximum size, minimum cladding thickness, minimum waveguide separation, and minimum bend radius. To couple light out-of-plane to a transmitter or receiver, a structure such as a vertical interconnect assembly (VIA) is required. For multimode waveguides the optimal placement of a total internal reflection mirror can be found without prior knowledge of the waveguide length. The optimal placement is found to be either 60 µm or 150 µm away from the end of the waveguide depending on which metric a designer wants to optimize the average output power, the output power variance, or the maximum possible power loss. For single mode waveguides a volume grating coupler is designed to couple light from a silicon waveguide to a polymer single mode waveguide. A focusing grating coupler is compared to a perpendicular grating coupler that is focused by a micro-molded lens. The focusing grating coupler had an optical loss of over -14 dB, while the grating coupler with a lens had an optical loss of -6.26 dB.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.

OPTIMAL SHAPE IN ELECTROMAGNETIC SCATTERING BY SMALL ASPHERICAL PARTICLES

We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.