This thesis examines the problem of load flow feasibility, in other words, the conditions under which a power network characterized by the load flow equations has a steady-state solution. In this thesis, we are particularly interested in load flow feasibility in the presence of extreme contingencies such as the outage of several transmission lines. / Denoting the load flow equations by z = f(x) where z is the vector of specified injections (the real and reactive bus demands, the specified real power bus generations and the specified bus voltage levels), the question addressed is whether there exists a real solution x to z = f( x) where x is the vector of unknown bus voltage magnitudes at load buses and unknown bus voltage phase angles at all buses but the reference bus. Attacking this problem via conventional load flow algorithms has a major drawback, principally the fact that such algorithms do not converge when the load flow injections z define or are close to defining an infeasible load flow. In such cases, lack of convergence may be due to load flow infeasibility or simply to the ill-conditioning of the load flow Jacobian matrix. / This thesis therefore makes use of the method of supporting hyperplanes to characterize the load flow feasibility region, defined as the set the injections z for which there exists a real solution x to the load flow equations. Supporting hyperplanes allow us to calculate the so-called load flow feasibility margin, which determines whether a given injection is feasible or not as well as measuring how close the injection is to the feasibility boundary. This requires solving a generalized eigenvalue problem and a corresponding optimization for the closest feasible boundary point to the given injection. / The effect of extreme network contingencies on the feasibility of a given injection is examined for two main cases: those contingencies that affect the feasibility region such as line outages and those that change the given injection itself such as an increase in VAR demand or the loss of a generator. The results show that the hyperplane method is a powerful tool for analyzing the effect of extreme contingencies on the feasibility of a power network.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

RAID systems (Redundant Arrays of Inexpensive Disks) have dominated backend storage systems for more than two decades and have grown continuously in size and complexity. Currently they face unprecedented challenges from data intensive applications such as image processing, transaction processing and data warehousing. As the size of RAID systems increases, designers are faced with both performance and reliability challenges. These challenges include limited back-end network bandwidth, physical interconnect failures, correlated disk failures and long disk reconstruction time. This thesis studies the scalability of RAID systems in terms of both performance and reliability through simulation, using a discrete event driven simulator for RAID systems (SIMRAID) developed as part of this project. SIMRAID incorporates two benchmark workload generators, based on the SPC-1 and Iometer benchmark specifications. Each component of SIMRAID is highly parameterised, enabling it to explore a large design space. To improve the simulation speed, SIMRAID develops a set of abstraction techniques to extract the behaviour of the interconnection protocol without losing accuracy. Finally, to meet the technology trend toward heterogeneous storage architectures, SIMRAID develops a framework that allows easy modelling of different types of device and interconnection technique.Simulation experiments were first carried out on performance aspects of scalability. They were designed to answer two questions: (1) given a number of disks, which factors affect back-end network bandwidth requirements; (2) given an interconnection network, how many disks can be connected to the system. The results show that the bandwidth requirement per disk is primarily determined by workload features and stripe unit size (a smaller stripe unit size has better scalability than a larger one), with cache size and RAID algorithm having very little effect on this value. The maximum number of disks is limited, as would be expected, by the back-end network bandwidth. Studies of reliability have led to three proposals to improve the reliability and scalability of RAID systems. Firstly, a novel data layout called PCDSDF is proposed. PCDSDF combines the advantages of orthogonal data layouts and parity declustering data layouts, so that it can not only survivemultiple disk failures caused by physical interconnect failures or correlated disk failures, but also has a good degraded and rebuild performance. The generating process of PCDSDF is deterministic and time-efficient. The number of stripes per rotation (namely the number of stripes to achieve rebuild workload balance) is small. Analysis shows that the PCDSDF data layout can significantly improve the system reliability. Simulations performed on SIMRAID confirm the good performance of PCDSDF, which is comparable to other parity declustering data layouts, such as RELPR. Secondly, a system architecture and rebuilding mechanism have been designed, aimed at fast disk reconstruction. This architecture is based on parity declustering data layouts and a disk-oriented reconstruction algorithm. It uses stripe groups instead of stripes as the basic distribution unit so that it can make use of the sequential nature of the rebuilding workload. The design space of system factors such as parity declustering ratio, chunk size, private buffer size of surviving disks and free buffer size are explored to provide guidelines for storage system design. Thirdly, an efficient distributed hot spare allocation and assignment algorithm for general parity declustering data layouts has been developed. This algorithm avoids conflict problems in the process of assigning distributed spare space for the units on the failed disk. Simulation results show that it effectively solves the write bottleneck problem and, at the same time, there is only a small increase in the average response time to user requests.