Optimal power flow (OPF) is the choice tool for determining the optimal operating status of the power system by managing controllable devices. The importance of the OPF approach has increased due to increasing energy prices and availability of more control devices. Existing OPF approaches exhibit shortcomings. Current OPF algorithms can be classified into (a) nonlinear programming, (b) intelligent search methods, and (c) sequential algorithms. Nonlinear programming algorithms focus on the solution of the Kuhn-Tucker conditions; they require a starting feasible solution and the model includes all constraints; these characteristics limit the robustness and efficiency of these methods. Intelligent search methods are first-order methods and are totally inefficient for large-scale systems. Traditional sequential algorithms require a starting feasible solution, a requirement that limits their robustness. Present implementations of sequential algorithms use traditional modeling that result in inefficient algorithms. The research described in this thesis has overcome the shortcomings by developing a robust and highly efficient algorithm. Robustness is defined as the ability to provide a solution for any system; the proposed approach achieves robustness by operating on suboptimal points and moving toward feasible, it stops at a suboptimal solution if an optimum does not exist. Efficiency is achieved by (a) converting the nonlinear OPF problem to a quadratic problem (b) and limiting the size of the model; the quadratic model enables fast convergence and the algorithm that identifies the active constraints, limits the size of the model by only including the active constraints. A concise description of the method is as follows: The proposed method starts from an arbitrary state which may be infeasible; model equations and system constraints are satisfied by introducing artificial mismatch variables at each bus. Mathematically this is an optimal but infeasible point. At each iteration, the artificial mismatches are reduced while the solution point maintains optimality. When mismatches reach zero, the solution becomes feasible and the optimum has been found; otherwise, the mismatch residuals are converted to load shedding and the algorithm provides a suboptimal but feasible solution. Therefore, the algorithm operates on infeasible but optimal points and moves towards feasibility. The proposed algorithm maximizes efficiency with two innovations: (a) quadratization that converts the nonlinear model to quadratic with excellent convergence properties and (b) minimization of model size by identifying active constraints, which are the only constraints included in the model. Finally sparsity technique is utilized that provide the best computational efficiency for large systems. This dissertation work demonstrates the proposed OPF algorithm using various systems up to three hundred buses and compares it with several well-known OPF software packages. The results show that the proposed algorithm converges fast and its runtime is competitive. Furthermore, the proposed method is extended to a three-phase OPF (TOPF) algorithm for unbalanced networks using the quadratized three-phase power system model. An example application of the TOPF is presented. Specifically, TOPF is utilized to address the problem of fault induced delayed voltage recovery (FIDVR) phenomena, which lead to unwanted relay operations, stalling of motors and load disruptions. This thesis presents a methodology that will optimally enhance the distribution system to mitigate/eliminate the onset of FIDVR. The time domain simulation method has been integrated with a TOPF model and a dynamic programming optimization algorithm to provide the optimal reinforcing strategy for the circuits.

Transformers are very important parts of any electrical network, and their size increase so does their price. Protecting these important devices is a daunting task due to the wide variety of operating conditions. This thesis develops a new protection scheme based on state estimation.The foundation upon which our protection scheme is built is the modeling of the single phase transformer system of equations. The transformer equations are composed of polynomial and differential equations and this system of equations involving the transformer's electrical quantities are modeled into a system of equations such that highest degree of each of the system's equations is quadratic―in a process named Quadratization and then integrated using a technique called Quadratic integration to give a set of algebraic companion equations that can be solved numerically to determine the health of the transformer.

This thesis discuss the possibility to position control a rotor levitated with active magnetic bearings. The controller type considered is model predictive control which is an online strategy that solves an optimization problem in every sample, making the model predictive controller computation-intense. Since the sampling time must be short to capture the dynamics of the rotor, very little time is left for the controller to perform the optimization. Different quadratic programming strategies are investigated to see if the problem can be solved in realtime. Additionally, the impact of the choices of prediction horizon, control horizon and terminal cost is discussed. Simulations showing the characteristics of these choises are made and the result is shown. / Det här examensarbetet diskuterar möjligheten att positionsreglera en rotor som leviteras på aktiva magnetlager. Reglerstrategin som används är modellbaserad prediktionsreglering vilket är en online-metod där ett optimeringsproblem löses i varje sampel. Detta gör att regulatorn blir mycket beräkningskrävande. Samplingstiden för systemet är mycket kort för att fånga dynamiken hos rotorn. Det betyder att regulatorn inte ges mycket tid att lösa optimeringsproblemet. Olika metoder för att lösa QP-problem betraktas för att se om det är möjligt att köra regulatorn i realtid. Dessutom diskuteras hur valet av prediktionshorisont, reglerhorisont och straff på sluttillståndet påverkar regleringen. Simuleringar som visar karakteristiken av dessa val har utförts.

This thesis evaluates decommissioning strategies for the International Space Station ISS. A permanent solution is attempted by employing energy efficient invariant manifolds that arise in the circular restricted three body problem CRTBP to transport the ISS from its low Earth orbit LEO to a lunar orbit. Although the invariant manifolds provide efficient transport, getting the the ISS onto the manifolds proves quite expensive, and the trajectories take too long to complete. Therefore a more practical, although temporary, solution consisting of an optimal re-boost maneuver with the European Space Agency's automated transfer vehicle ATV is proposed. The optimal re-boost trajectory is found using control parameterization and the sequential quadratic programming SQP algorithm. The model used for optimization takes into account the affects of atmospheric drag and gravity perturbations. The optimal re-boost maneuver produces a satellite lifetime of approximately ninety-five years using a two ATV strategy.

In this master thesis, control algoritms using arm side sensors are investigated for an industrial robot. The sensors can be position encoders placed after the gearbox and accelerometers on the robot arms. Control strategies are discussed and evaluated for different models of the robot, after which chosen strategies are applied to a realistic model. Control algoritms using arm side sensors (LQ, dual-loop and PD-PID) are compared to a PID-controller that only uses measurements of motor position for feedback control. The comparison are done with respect to disturbance rejection, oscillation damping, robustness and tracking performance of a reference trajectory. Results from tests with the realistic robot modell shows that disturbance rejection was improved a factor 2 to 5 while tracking performance was improved a factor 4 to 5 according to maximum deviation from the reference path. At the same time good re-sults are achieved regarding oscillation damping and robustness.

There are two main approaches to robust stability analysis: the input-output stability framework with scaling or multiplier, and the Lyapunov functions. Analysis methods in these two directions are usually developed independently, and the relationship between the two is not clear except for some special cases. This motivates us to study the relationship between the two approaches. The generalized performance problem refers to certain frequency-domain conditions on a transfer matrix. We prove the equivalent relationship between generalized performance and robust stability under certain assumptions. The definition of generalized performance requires the internal stability of a transfer matrix, which is not a necessity for robust stability. In view of this, we derive new frequency-domain conditions for robust stability without this requirement. Our result contains a version of the circle criterion as a special case. To tackle the generalized performance problem, we propose a version of the Kalman-Yakubovich-Popov (KYP) lemma to transform the frequency-domain conditions into linear matrix inequalities (LMIs). The proposed LMI condition is then connected to the quadratic stability of an uncertain linear system. Combining the derived results gives a clear picture of the relationships between robust stability, generalized performance, quadratic stability, and KYP lemma. The connections not only unify some previous results but also extend those results to more general stability regions and types of uncertainty. In addition to robust stability analysis, we also tackle the corresponding synthesis problem, i.e. robust pole placement. The desired region for robust pole placement can be the intersection or the union of simple regions. (Simple regions are the half plane, the disk, and the outside of a disk.) One contribution of our synthesis result is that the desired region can be non-convex¡Xmost results on robust pole placement focus on convex regions only. Two examples of the longitudinal control of a combat aircraft and the attitude control of a satellite demonstrate the effectiveness of our result.

In 2010, Prof. Chang and Prof. Lee applied Lagrange interpolation formula to decode a class of binary cyclic codes, but they did not provide an effective way to calculate the Lagrange interpolation formula. In this thesis, we use the least common multiple of polynomials to compute it effectively. Let E be an extension field of degree m over F = F_p and £] be a primitive nth root of unity in E. For a nonzero element r in E, the minimal polynomial of r over F is denoted by m_r(x). Then, let Min (r, F) denote the least common multiple of m_r£]^i(x) for i = 0, 1,..., n-1 and be called the generalized minimal polynomial of over F. For any binary quadratic residue code mentioned in this thesis, the set of all its correctable error patterns can be partitioned into root sets of some generalized minimal polynomials over F. Based on this idea, we can develop an effective method to calculate the Lagrange interpolation formula.

The exact D-optimal design problems for regression models has been in-vestigated in many literatures. Huang (1987) and Gaffke (1987) provided a sufficient condition for the minimum sample size for an certain set of candidate designs to be exact D-optimal for polynomial regression models on a compact interval. In this work we consider a mixture experiment with q nonnegative components, where the proportions of components are sub- ject to the simplex restriction $sum_{i=1}^q x_i =1$, $x_i ¡Ù 0$. The exact D-optimal designs for mixture experiments for Scheffe¡¦s quadratic models are investigated. Based on results in Kiefer (1961) results about the exact D-optimal designs for mixture models with two or three ingredients are provided and numerical verifications for models with ingredients between four and nine are presented.

The aim of this study was to investigate the effects of using interactive whiteboard and computer technology on graduate language and mathematics student&rsquo / performance in quadratic equation functions graphics. Two groups of language and mathematics graduate students were selected for the study / one for experimental group and the other for control group. The experimental group consists of 32 students, and control group consists of 33 students. The control group is thought by traditional learning whereas the experimental group is thought the same topic by interactive whiteboard and computer technology. Graphic Achievement Test (GAT), Attitudes toward Technology Scale (ATTS) and Attitude toward Mathematics Scale (ATMS) and interviews were used as a data collection instruments. GAT applied as a pre-test, post-test and delayed post-test on both of the groups. However the attitudes scales applied only experimental group before and after the treatment.

Gun and gun turret systems are the primary units of the weapon systems of an aircraft. They are required to hit targets accurately during operations. That is why a complete, high precision control of weapon systems is required. This function is provided by accurate modeling of the system and the design of a suitable controller. This study presents the modeling of and controller design for the gun and turret system for an aircraft. For the controller design purpose, first the mathematical model of the system is constructed. Then the controller is designed to position the turret system as the target comes into sight. The reference input to the controller will either be obtained from a FLIR (Forward Looking Infrared) unit or from a HCU (Hand Control Unit). The basic specification for the controller is to hold theerror signal within the 5.5&deg / positioning envelope. This specification is satisfied by designing Linear Quadratic Gaussian and Internal Model Control type controllers. The performance of the overall system has been examined both by simulation studies and on the real physical system. Results have shown that the designed system is well over being sufficient.