A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia

Performance study of two different compensating devices in a custom power park

Simulation study of a custom power park (CPP) is presented. It is assumed that the park contains unbalanced and nonlinear loads in addition to a sensitive load. Two different types of compensators are used separately to protect the sensitive load against unbalance and distortion caused by the other loads. It has been shown that a shunt compensator can regulate the voltage of the CPP bus, whereas the series compensator can only regulate the sensitive load terminal voltage. Additional issues such as the load transfer through a static transfer switch, detection of sag/fault etc. are also discussed. The concepts are validated through PSCAD/EMTDC simulation studies on a sample distribution system.

Parallel linear system solution and its application to railway power network simulation

The Streaming SIMD extension (SSE) is a special feature embedded in the Intel Pentium III and IV classes of microprocessors. It enables the execution of SIMD type operations to exploit data parallelism. This article presents improving computation performance of a railway network simulator by means of SSE. Voltage and current at various points of the supply system to an electrified railway line are crucial for design, daily operation and planning. With computer simulation, their time-variations can be attained by solving a matrix equation, whose size mainly depends upon the number of trains present in the system. A large coefficient matrix, as a result of congested railway line, inevitably leads to heavier computational demand and hence jeopardizes the simulation speed. With the special architectural features of the latest processors on PC platforms, significant speed-up in computations can be achieved.

Numerical models to simulate the thermal performance of LSF wall panels

Fire safety of buildings has been recognised as very important by the building industry and the community at large. Gypsum plasterboards are widely used to protect light gauge steel frame (LSF) walls all over the world. Gypsum contains free and chemically bound water in its crystal structure. Plasterboard also contains gypsum (CaSO4.2H2O) and calcium carbonate (CaCO3). The dehydration of gypsum and the decomposition of calcium carbonate absorb heat, and thus are able to protect LSF walls from fires. Kolarkar and Mahendran (2008) developed an innovative composite wall panel system, where the insulation was sandwiched between two plasterboards to improve the thermal and structural performance of LSF wall panels under fire conditions. In order to understand the performance of gypsum plasterboards and LSF wall panels under standard fire conditions, many experiments were conducted in the Fire Research Laboratory of Queensland University of Technology (Kolarkar, 2010). Fire tests were conducted on single, double and triple layers of Type X gypsum plasterboards and load bearing LSF wall panels under standard fire conditions. However, suitable numerical models have not been developed to investigate the thermal performance of LSF walls using the innovative composite panels under standard fire conditions. Continued reliance on expensive and time consuming fire tests is not acceptable. Therefore this research developed suitable numerical models to investigate the thermal performance of both plasterboard assemblies and load bearing LSF wall panels. SAFIR, a finite element program, was used to investigate the thermal performance of gypsum plasterboard assemblies and LSF wall panels under standard fire conditions. Appropriate values of important thermal properties were proposed for plasterboards and insulations based on laboratory tests, literature review and comparisons of finite element analysis results of small scale plasterboard assemblies from this research and corresponding experimental results from Kolarkar (2010). The important thermal properties (thermal conductivity, specific heat capacity and density) of gypsum plasterboard and insulation materials were proposed as functions of temperature and used in the numerical models of load bearing LSF wall panels. Using these thermal properties, the developed finite element models were able to accurately predict the time temperature profiles of plasterboard assemblies while they predicted them reasonably well for load bearing LSF wall systems despite the many complexities that are present in these LSF wall systems under fires. This thesis presents the details of the finite element models of plasterboard assemblies and load bearing LSF wall panels including those with the composite panels developed by Kolarkar and Mahendran (2008). It examines and compares the thermal performance of composite panels developed based on different insulating materials of varying densities and thicknesses based on 11 small scale tests, and makes suitable recommendations for improved fire performance of stud wall panels protected by these composite panels. It also presents the thermal performance data of LSF wall systems and demonstrates the superior performance of LSF wall systems using the composite panels. Using the developed finite element of models of LSF walls, this thesis has proposed new LSF wall systems with increased fire rating. The developed finite element models are particularly useful in comparing the thermal performance of different wall panel systems without time consuming and expensive fire tests.

Thermal performance of non-load bearing LSF walls using numerical studies

Fire safety of light gauge cold-formed steel frame (LSF) wall systems is significant to the build-ing design. Gypsum plasterboard is widely used as a fire safety material in the building industry. It contains gypsum (CaSO4.2H2O), Calcium Carbonate (CaCO3) and most importantly free and chemically bound water in its crystal structure. The dehydration of the gypsum and the decomposition of Calcium Carbonate absorb heat, which gives the gypsum plasterboard fire resistant qualities. Recently a new composite panel system was developed, where a thin insulation layer was used externally between two plasterboards to improve the fire performance of LSF walls. In this research, finite element thermal models of both the traditional LSF wall panels with cavity insulation and the new LSF composite wall panels were developed to simulate their thermal behaviour under standard and realistic design fire conditions. Suitable thermal properties of gypsum plaster-board, insulation materials and steel were used. The developed models were then validated by comparing their results with fire test results. This paper presents the details of the developed finite element models of non-load bearing LSF wall panels and the thermal analysis results. It has shown that finite element models can be used to simulate the thermal behaviour of LSF walls with varying configurations of insulations and plasterboards. The results show that the use of cavity insulation was detrimental to the fire rating of LSF walls while the use of external insulation offered superior thermal protection. Effects of real fire conditions are also presented.

Effects of various power system stabilizers on improving power system dynamic performance

To ensure the small-signal stability of a power system, power system stabilizers (PSSs) are extensively applied for damping low frequency power oscillations through modulating the excitation supplied to synchronous machines, and increasing interest has been focused on developing different PSS schemes to tackle the threat of damping oscillations to power system stability. This paper examines four different PSS models and investigates their performances on damping power system dynamics using both small-signal eigenvalue analysis and large-signal dynamic simulations. The four kinds of PSSs examined include the Conventional PSS (CPSS), Single Neuron based PSS (SNPSS), Adaptive PSS (APSS) and Multi-band PSS (MBPSS). A steep descent parameter optimization algorithm is employed to seek the optimal PSS design parameters. To evaluate the effects of these PSSs on improving power system dynamic behaviors, case studies are carried out on an 8-unit 24-bus power system through both small-signal eigenvalue analysis and large-signal time-domain simulations.

Thermal performance of composite panels under fire conditions using numerical studies : plasterboards, rockwool, glass fibre and cellulose insulations

In recent times, light gauge steel frame (LSF) wall systems are increasingly used in the building industry. They are usually made of cold-formed and thin-walled steel studs that are fire-protected by two layers of plasterboard on both sides. A composite LSF wall panel system was developed recently, where an insulation layer was used externally between the two plasterboards to improve the fire performance of LSF wall panels. In this research, finite element thermal models of the new composite panels were developed using a finite element program, SAFIR, to simulate their thermal performance under both standard and Eurocode design fire curves. Suitable apparent thermal properties of both the gypsum plasterboard and insulation materials were proposed and used in the numerical models. The developed models were then validated by comparing their results with available standard fire test results of composite panels. This paper presents the details of the finite element models of composite panels, the thermal analysis results in the form of time-temperature profiles under standard and Eurocode design fire curves and their comparisons with fire test results. Effects of using rockwool, glass fibre and cellulose fibre insulations with varying thickness and density were also investigated, and the results are presented in this paper. The results show that the use of composite panels in LSF wall systems will improve their fire rating, and that Eurocode design fires are likely to cause severe damage to LSF walls than standard fires.

Performance comparison of four power system stabilizer

The well-known power system stabilizer (PSS) is used to generate supplementary control signals for the excitation system of a generator so as to damp low frequency oscillations in the power system concerned. Up to now, various kinds of PSS design methods have been proposed and some of them applied in actual power systems with different degrees. Given this background, the small-disturbance eigenvalue analysis and large-disturbance dynamic simulations in the time domain are carried out to evaluate the performances of four different PSS design methods, including the Conventional PSS (CPSS), Single-Neuron PSS (SNPSS), Adaptive PSS (APSS) and Multi-band PSS (MBPSS). To make the comparisons equitable, the parameters of the four kinds of PSSs are all determined by the steepest descent method. Finally, an 8-unit 24-bus power system is employed to demonstrate the performances of the four kinds of PSSs by the well-established eigenvalue analysis as well as numerous digital simulations, and some useful conclusions obtained.

Thermal performance of load bearing cold-formed steel walls under fire conditions using numerical studies

Cold–formed Light gauge Steel Frame (LSF) wall systems are increasingly used in low-rise and multi-storey buildings and hence their fire safety has become important in the design of buildings. A composite LSF wall panel system was developed recently, where a thin insulation was sandwiched between two plasterboards to improve the fire performance of LSF walls. Many experimental and numerical studies have been undertaken to investigate the fire performance of non-load bearing LSF wall under standard conditions. However, only limited research has been undertaken to investigate the fire performance of load bearing LSF walls under standard and realistic design fire conditions. Therefore in this research, finite element thermal models of both the conventional load bearing LSF wall panels with cavity insulation and the innovative LSF composite wall panel were developed to simulate their thermal behaviour under standard and realistic design fire conditions. Suitable thermal properties were proposed for plasterboards and insulations based on laboratory tests and available literature. The developed models were then validated by comparing their results with available fire test results of load bearing LSF wall. This paper presents the details of the developed finite element models of load bearing LSF wall panels and the thermal analysis results. It shows that finite element models can be used to simulate the thermal behaviour of load bearing LSF walls with varying configurations of insulations and plasterboards. Failure times of load bearing LSF walls were also predicted based on the results from finite element thermal analyses. Finite element analysis results show that the use of cavity insulation was detrimental to the fire rating of LSF walls while the use of external insulation offered superior thermal protection to them. Effects of realistic design fire conditions are also presented in this paper.

Numerical modelling and analysis of the blast performance of laminated glass panels and the influence of material parameters

This paper presents a comprehensive numerical procedure to treat the blast response of laminated glass (LG) panels and studies the influence of important material parameters. Post-crack behaviour of the LG panel and the contribution of the interlayer towards blast resistance are treated. Modelling techniques are validated by comparing with existing experimental results. Findings indicate that the tensile strength of glass considerably influences the blast response of LG panels while the interlayer material properties have a major impact on the response under higher blast loads. Initially, glass panes absorb most of the blast energy, but after the glass breaks, interlayer deforms further and absorbs most of the blast energy. LG panels should be designed to fail by tearing of the interlayer rather than failure at the supports to achieve a desired level of protection. From this aspect, material properties of glass, interlayer and sealant joints play important roles, but unfortunately they are not accounted for in the current design standards. The new information generated in this paper will enhance the capabilities of engineers to better design LG panels under blast loads and use better materials to improve the blast response of LG panels.

Fire performance of LSF wall panels using numerical parametric studies

Light Gauge Steel Framing (LSF) walls made of cold-formed and thin-walled steel lipped channel studs with plasterboard linings on both sides are commonly used in commercial, industrial and residential buildings. However, there is limited data about their structural and thermal performances under fire conditions. Recent research at the Queensland University of Technology has investigated the structural and thermal behaviour of load bearing LSF wall systems. In this research a series of full scale fire tests was conducted first to evaluate the performance of LSF wall systems with eight different wall configurations under standard fire conditions. Finite element models of LSF walls were then developed, analysed under transient and steady state conditions, and validated using full scale fire tests. This paper presents the details of an investigation into the fire performance of LSF wall panels based on an extensive finite element analysis based parametric study. The LSF wall panels with eight different plasterboard-insulation configurations were considered under standard fire conditions. Effects of varying steel grades, steel thicknesses, screw spacing, plasterboard restraint, insulation materials and load ratio on the fire performance of LSF walls were investigated and the results of extensive fire performance data are presented in the form of load ratio versus time and critical hot flange (failure) temperature curves.

Automated power semiconductor switching performance feature extraction from experimental double-pulse waveform data

Double-pulse tests are commonly used as a method for assessing the switching performance of power semiconductor switches in a clamped inductive switching application. Data generated from these tests are typically in the form of sampled waveform data captured using an oscilloscope. In cases where it is of interest to explore a multi-dimensional parameter space and corresponding result space it is necessary to reduce the data into key performance metrics via feature extraction. This paper presents techniques for the extraction of switching performance metrics from sampled double-pulse waveform data. The reported techniques are applied to experimental data from characterisation of a cascode gate drive circuit applied to power MOSFETs.