This dissertation attempts to establish an analytical and comprehensive framework to deal with two critical challenges associated with voltage stability analysis: 1. To study the new competitive environment appropriately and give more incentive for reactive power supports, one has to evaluate the impacts of distributed market forces on voltage stability, which complicates the voltage stability analysis. 2. Accurately estimating voltage stability margin online is always the goal of the industry. Industry used to apply static analysis for its computation speed at the cost of losing accuracy. On the other hand, dynamic analysis can result in more accurate estimation, but generally has a huge computation cost. So a challenge is to estimate the voltage stability margin accurately and efficiently at a reasonable cost, especially for large system. Considering the first challenge, this dissertation applied eigenvalue based bifurcation analysis to allocate the contribution of voltage stability. We investigate how parameters of the system influence the bifurcations. Three bifurcations (singularity induced bifurcation, saddle-node and Hopf bifurcation) and their relationship to several commonly used controllers are analyzed. Their parameters’ impact on these bifurcations have been investigated, from which we found a way to allocate the contribution by analyzing the relative positions of the bifurcations. For the second challenge, a new fast numerical scheme is developed to estimate voltage stability margin by intelligently adjusting the load increase ratio. A criterion, named EMD (Equilibrium Manifold Deviation) criterion, is proposed to gauge the accuracy of the estimation. And based on this criterion, a new computation scheme is proposed. The validity of our new approach is proven based on the well-known Runge-Kutta-Fehlberg method, and can be extended to other explicit single-step methods easily. Numerical tests demonstrate that the new approach is very practical and has great potential for industrial applications. This dissertation extends our new numerical scheme to stiff systems. When a system is ill-conditioned, the implicit method would be applied to achieve numerical stability. We further demonstrate the validity to combine the intelligent load adjustment technique with the implicit method to save the computation cost without loss of accuracy. This dissertation also delves into the auto detection of stiffness of the power system, and extends our new numerical scheme to general sytems.

We examine steady transonic flows of Bethe-Zel\'dovich-Thompson (BZT) fluids over thin turbine blades or airfoils. BZT fluids are ordinary fluids having a region of negative fundamental derivative over a finite range of pressures and temperatures in the single phase regime. We derive the transonic small disturbance equation (TSDE) capable of capturing the qualitative behavior of BZT fluids. The shock jump conditions, and shock existence conditions consistent with the derived TSDE are presented. The flux function is seen to be quartic in the pressure or density perturbation rather than the quadratic (convex) flux function of the perfect gas theory. We show how this nonconvex flux function can be used to predict and explain the complex flows possible in transonic BZT fluids. Numerical solutions using a successive line relaxation (SLR) scheme are presented. New results of interest include shock-splitting, collisions between expansion and compression shocks, the prediction and observation of two compressive bow shocks in supersonic flows, and the observation of as many as three normal stern shocks following an oblique trailing edge shock. / Master of Science

Um método de correção viscosa é aplicado na solução da equação potencial transônica de pequenas perturbações (TSD) no domínio da frequência. O objetivo é melhorar os resultados transônicos em que a interação choque/camada-limite é importante. A espessura de deslocamento da camada limite é estimada, a partir dos resultados da análise do escoamento invíscido, usando um método integral. A espessura de deslocamento é usada, então, para modificar a geometria das superfícies de sustentação e um novo resultado invíscido é obtido. Esse processo é repetido até que se atinja a convergência. No passado esse método foi aplicado, com bons resultados, na análise no domínio do tempo. No domínio da frequência os termos espaciais não lineares são preservados usando uma técnica de transformação conhecida como média harmônica. A principal razão para usar equação TSD ainda é o custo computacional, especialmente em se tratando de configurações completas de aeronaves. Um código de computador original é desenvolvido para análise bidimensional e um código de computador tridimensional existente é modificado para incluir a correção viscosa. A equação TSD é aproximada usando o método das diferenças finitas e resolvida usando sobre-relaxação sucessiva por linhas. Nos dois códigos é utilizada correção para vorticidade e variação de entropia. Os resultados têm boa correlação com dados experimentais publicados para a distribuição de pressão em regime transônico estacionário. / A viscous correction method is applied to the solution of the transonic small disturbance (TSD) potential equation in the frequency domain. The objective is to improve transonic results for which shock/boundary-layer interaction is important. Boundary-layer displacement thickness is calculated, with an integral method, using the results from an inviscid flow analysis. The calculated displacement thickness is then used to modify the lifting surface geometry and a new inviscid result is obtained. This process is repeated until convergence is achieved. In the past that method has been applied to time domain analysis with good results. In frequency domain the spatial nonlinear terms are preserved using a transformation technique known as harmonic averaging. The main reason for using the TSD equation still is computational cost, especially when dealing with complete aircraft configurations. An original computer code is developed for two-dimensional analysis and an existing three-dimensional computer code is extended to include the viscous correction. The transonic small disturbance potential equation is approximated using the finite difference method and solved through successive line over-relaxation. Both codes include correction for vorticity and variation in entropy. Results for several airfoil sections are obtained. The results compare well with published experimental data for steady transonic pressure distribution.

Um método de correção viscosa é aplicado na solução da equação potencial transônica de pequenas perturbações (TSD) no domínio da frequência. O objetivo é melhorar os resultados transônicos em que a interação choque/camada-limite é importante. A espessura de deslocamento da camada limite é estimada, a partir dos resultados da análise do escoamento invíscido, usando um método integral. A espessura de deslocamento é usada, então, para modificar a geometria das superfícies de sustentação e um novo resultado invíscido é obtido. Esse processo é repetido até que se atinja a convergência. No passado esse método foi aplicado, com bons resultados, na análise no domínio do tempo. No domínio da frequência os termos espaciais não lineares são preservados usando uma técnica de transformação conhecida como média harmônica. A principal razão para usar equação TSD ainda é o custo computacional, especialmente em se tratando de configurações completas de aeronaves. Um código de computador original é desenvolvido para análise bidimensional e um código de computador tridimensional existente é modificado para incluir a correção viscosa. A equação TSD é aproximada usando o método das diferenças finitas e resolvida usando sobre-relaxação sucessiva por linhas. Nos dois códigos é utilizada correção para vorticidade e variação de entropia. Os resultados têm boa correlação com dados experimentais publicados para a distribuição de pressão em regime transônico estacionário. / A viscous correction method is applied to the solution of the transonic small disturbance (TSD) potential equation in the frequency domain. The objective is to improve transonic results for which shock/boundary-layer interaction is important. Boundary-layer displacement thickness is calculated, with an integral method, using the results from an inviscid flow analysis. The calculated displacement thickness is then used to modify the lifting surface geometry and a new inviscid result is obtained. This process is repeated until convergence is achieved. In the past that method has been applied to time domain analysis with good results. In frequency domain the spatial nonlinear terms are preserved using a transformation technique known as harmonic averaging. The main reason for using the TSD equation still is computational cost, especially when dealing with complete aircraft configurations. An original computer code is developed for two-dimensional analysis and an existing three-dimensional computer code is extended to include the viscous correction. The transonic small disturbance potential equation is approximated using the finite difference method and solved through successive line over-relaxation. Both codes include correction for vorticity and variation in entropy. Results for several airfoil sections are obtained. The results compare well with published experimental data for steady transonic pressure distribution.

This thesis is devoted to the development of new approaches for control coordination of PSSs (power system stabilisers) and FACTS (flexible alternating current transmission system) devices for achieving and enhancing small-disturbance stability in multi-machine power systems. The key objectives of the research reported in the thesis are, through optimal control coordination of PSSs and/or FACTS devices, those of maintaining satisfactory power oscillation damping and secure system operation when the power system is subject to persisting disturbances in the form of load demand fluctuations and switching control. Although occurring less frequently, fault disturbances are also considered in the assessment of the control coordination performance. Based on the constrained optimisation method in which the eigenvalue-based objective function is minimised to identify the optimal parameters of power system damping controllers, the thesis first develops a procedure for designing the control coordination of PSSs and FACTS devices controllers. The eigenvalue-eigenvector equations associated with the selected electromechanical modes form a set of equality constraints in the optimisation. The key advance of the procedure is that there is no need for any special software system for eigenvalue calculations, and the use of sparse Jacobian matrix for forming the eigenvalue-eigenvector equations leads to the sparsity formulation which is essential for large power systems. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation, using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. On recognising that the fixed-parameter controllers, even when designed with optimal control coordination, have an inherent limitation which precludes optimal system damping for each and every possible system operating condition, the second part of ii the research has a focus on adaptive control techniques and their applications to power system controllers. In this context, the thesis reports the development of a new design procedure for online control coordination which leads to adaptive PSSs and/or supplementary damping controllers (SDCs) of FACTS devices for enhancing the stability of the electromechanical modes in a multi-machine power system. The controller parameters are adaptive to the changes in system operating condition and/or configuration. Central to the design is the use of a neural network synthesised to give in its output layer the optimal controller parameters adaptive to system operating condition and configuration. A novel feature of the neural adaptive controller is that of representing the system configuration by a reduced nodal impedance matrix which is input to the neural network.

An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.