No presente trabalho são apresentados resultados de simulação numérica transiente de um sistema de refrigeração doméstico de compressão a vapor considerando o procedimento descrito por JAKOBSEN (1995). O modelo matemático empregado se baseia num sistema de equações algébrico-diferenciais (EAD) de primeira ordem, obtido a partir do balanço de energia nos diferentes componentes do sistema de refrigeração, e de algumas outras relações necessárias para simular o comportamento global do sistema de refrigeração. O sistema de equações resultante é resolvido numericamente no software livre WinDali, da Universidade Técnica de Dinamarca. Dito software permite resolver sistemas de EADs que apresentam descontinuidades matemáticas usando o método de Runge- Kutta de quarta ordem. O modelo matemático empregado permite calcular a eficiência do sistema de refrigeração, predizer o consumo de energia, caracterizar termodinamicamente o sistema de refrigeração e suas interações, e descrever quantitativamente as perdas termodinâmicas (geração de entropia) do sistema funcionando em regime de operação. Esses resultados são obtidos em função da estratégia de controle do compressor, eficiência do compressor e do dimensionamento dos diferentes componentes do sistema de refrigeração. Os resultados comprovam que o modelo matemático e o programa computacional empregados permitem descrever corretamente o comportamento de um sistema de refrigeração doméstico, resultando numa ferramenta muito útil para otimização de refrigeradores domésticos. / In the present work are presented transient numerical simulation results of a vapor compression domestic refrigeration system considering the procedure described by JAKOBSEN (1995). The employed mathematical model is based on first order differential-algebraic equation (DAE) systems, obtained from energy balance in the different components of the refrigeration system, and from others relations that are necessary to simulate the global behavior of a refrigeration system. The resulting equation system is solved numerically in the free software WinDali developed at Technical University of Denmark. This software allows solving DAE systems that present mathematical discontinuities, using the Runge-Kutta method of fourth order. The employed mathematical model allows calculating the refrigeration system efficiency, predict the energy consumption, thermodynamically characterize the refrigeration system and its interactions and quantitatively describe the thermodynamic losses (entropy generation) of the system running in the operation regime. These results are obtained as a function of the compressor control strategy, compressor efficiency, and sizing of different components of the refrigeration system. The results confirm that the mathematical model and the computational program allow describing correctly the behavior of a domestic refrigeration system, resulting in a very useful tool for optimization of domestic refrigerators.

With the increased complexity of modern power systems, it may be required more than one platform to do an intended study efficiently and accurately. This research was carried out to investigate the use of co-simulation in an application of power system. A back-to-back Voltage Source Converter (VSC) transmission system was modeled in PSCAD/EMTDC which is an Electro-Magnetic Type (EMT) software. Results were analyzed for some operating points of the system. Then the control system of the above system was modelled in MATLAB/SIMULINK while the rest of the system was modeled in PSCAD/EMTDC. Both of these systems were interfaced to obtain the complete system and results were analyzed under same operating points as the original PSCAD case.

This thesis presents a new way of combining non-linear optimization algorithms and electromagnetic transient (EMT) simulation. In this new combination, a non-linear optimization algorithm utilizes a real-time EMT simulation environment as objective function evaluator. However, as more applications of the off-line EMT simulation software implementation were made, the combination between non-linear optimization algorithms and off-line EMT simulation software revealed new need, which this research work attempts to address. The first need arose from the speed of simulation of the off-line EMT simulation software. With a certain breed of non-linear optimization algorithms, heuristics bases algorithms in particular, a large number of objective function evaluations are required before the termination or convergence criterion in the selected algorithms is satisfied. Sometimes, the number of evaluations as well as the complexity of the simulation case where the objective function is based upon translates into a very long simulation time, which goes beyond the boundary of given resources. This research work attempts to address this simulation timing issue by capitalizing on the real timeness of the simulation environment as well as utilizing the multiple instances of the simulation environment in parallel. The second need arose from the modeling requirement of the off-line EMT simulation software. In order to properly design the necessary objective function evaluator, which is largely a simulation case, a large amount of information needs to be embedded into the case. Under certain circumstances, the necessary information would not be available. Therefore, the simulation case needs to include approximations which may cause compromise in the end result. This limitation becomes more obvious when a real world device such as a commercial controller becomes involved. On the contrary, this limitation can be addressed by the real-time simulation environment because this environment can be directly interfaced with the real world device. In this way, the need for detailed information regarding the device is eliminated. This elimination would enlarge the application of the combination, between the non-linear optimization algorithm and EMT type simulation environment. The effectiveness of the proposed approach is demonstrated by various examples throughout this thesis.

This thesis presents the application of graphics processing unit (GPU) based parallel computing technique to speed up electromagnetic transients (EMT) simulation of large power systems. GPUs support extra computing capability to handle gaming and animation related applications in the desktop computers. GPUs can be used for general-purpose computations, such as EMT simulation. Traditionally, EMT simulation tools are implemented on the CPUs, where simulation is performed in a sequential manner. Hence, with the increase in network size, there is a drastic increase in simulation times. This research shows that the use of GPU computing considerably reduces the total simulation time. This thesis proposes parallelized algorithm for EMT simulations on the GPU, and demonstrates the algorithm by simulating large power systems. Total computation times for GPU computing, using 'compute unified device architecture' (CUDA)-based C programming are compared with the total computation times for the sequential implementations on the CPU using ANSI-C programming for systems of various sizes and types. Special parallel processing techniques are implemented to model various power system components such as transmission lines, generators, etc. An advanced technique to implement parallel matrix-vector multiplication on the GPU is implemented, which shows a significant performance gain in the simulation. A sparsity-based technique for the inverse admittance matrix is implemented in this simulation process to ignore the multiplications involving zeros. A typical power electronic subsystem is also implemented in this simulation process, which had not been implemented in the literature so far for the GPU platforms. GPU computing-based simulation of large power networks with many power electronic subsystems has shown a massive performance gain compared to conventional sequential simulations with and without the sparsity technique. Finally, in this research work, the effect of granularity on the speedup of simulation was investigated. Granularity is defined as the ratio of the number of transmission lines used to interconnect various subsystems to the total size of the network. It should be noted that dividing a network into smaller subsystems requires additional transmission lines. Simulation results show that there is a negative impact on the overall performance gain of simulation with the use of excessive transmission lines in the test systems.

With the increased complexity of modern power systems, it may be required more than one platform to do an intended study efficiently and accurately. This research was carried out to investigate the use of co-simulation in an application of power system. A back-to-back Voltage Source Converter (VSC) transmission system was modeled in PSCAD/EMTDC which is an Electro-Magnetic Type (EMT) software. Results were analyzed for some operating points of the system. Then the control system of the above system was modelled in MATLAB/SIMULINK while the rest of the system was modeled in PSCAD/EMTDC. Both of these systems were interfaced to obtain the complete system and results were analyzed under same operating points as the original PSCAD case.

This thesis presents a new way of combining non-linear optimization algorithms and electromagnetic transient (EMT) simulation. In this new combination, a non-linear optimization algorithm utilizes a real-time EMT simulation environment as objective function evaluator. However, as more applications of the off-line EMT simulation software implementation were made, the combination between non-linear optimization algorithms and off-line EMT simulation software revealed new need, which this research work attempts to address. The first need arose from the speed of simulation of the off-line EMT simulation software. With a certain breed of non-linear optimization algorithms, heuristics bases algorithms in particular, a large number of objective function evaluations are required before the termination or convergence criterion in the selected algorithms is satisfied. Sometimes, the number of evaluations as well as the complexity of the simulation case where the objective function is based upon translates into a very long simulation time, which goes beyond the boundary of given resources. This research work attempts to address this simulation timing issue by capitalizing on the real timeness of the simulation environment as well as utilizing the multiple instances of the simulation environment in parallel. The second need arose from the modeling requirement of the off-line EMT simulation software. In order to properly design the necessary objective function evaluator, which is largely a simulation case, a large amount of information needs to be embedded into the case. Under certain circumstances, the necessary information would not be available. Therefore, the simulation case needs to include approximations which may cause compromise in the end result. This limitation becomes more obvious when a real world device such as a commercial controller becomes involved. On the contrary, this limitation can be addressed by the real-time simulation environment because this environment can be directly interfaced with the real world device. In this way, the need for detailed information regarding the device is eliminated. This elimination would enlarge the application of the combination, between the non-linear optimization algorithm and EMT type simulation environment. The effectiveness of the proposed approach is demonstrated by various examples throughout this thesis.

No presente trabalho são apresentados resultados de simulação numérica transiente de um sistema de refrigeração doméstico de compressão a vapor considerando o procedimento descrito por JAKOBSEN (1995). O modelo matemático empregado se baseia num sistema de equações algébrico-diferenciais (EAD) de primeira ordem, obtido a partir do balanço de energia nos diferentes componentes do sistema de refrigeração, e de algumas outras relações necessárias para simular o comportamento global do sistema de refrigeração. O sistema de equações resultante é resolvido numericamente no software livre WinDali, da Universidade Técnica de Dinamarca. Dito software permite resolver sistemas de EADs que apresentam descontinuidades matemáticas usando o método de Runge- Kutta de quarta ordem. O modelo matemático empregado permite calcular a eficiência do sistema de refrigeração, predizer o consumo de energia, caracterizar termodinamicamente o sistema de refrigeração e suas interações, e descrever quantitativamente as perdas termodinâmicas (geração de entropia) do sistema funcionando em regime de operação. Esses resultados são obtidos em função da estratégia de controle do compressor, eficiência do compressor e do dimensionamento dos diferentes componentes do sistema de refrigeração. Os resultados comprovam que o modelo matemático e o programa computacional empregados permitem descrever corretamente o comportamento de um sistema de refrigeração doméstico, resultando numa ferramenta muito útil para otimização de refrigeradores domésticos. / In the present work are presented transient numerical simulation results of a vapor compression domestic refrigeration system considering the procedure described by JAKOBSEN (1995). The employed mathematical model is based on first order differential-algebraic equation (DAE) systems, obtained from energy balance in the different components of the refrigeration system, and from others relations that are necessary to simulate the global behavior of a refrigeration system. The resulting equation system is solved numerically in the free software WinDali developed at Technical University of Denmark. This software allows solving DAE systems that present mathematical discontinuities, using the Runge-Kutta method of fourth order. The employed mathematical model allows calculating the refrigeration system efficiency, predict the energy consumption, thermodynamically characterize the refrigeration system and its interactions and quantitatively describe the thermodynamic losses (entropy generation) of the system running in the operation regime. These results are obtained as a function of the compressor control strategy, compressor efficiency, and sizing of different components of the refrigeration system. The results confirm that the mathematical model and the computational program allow describing correctly the behavior of a domestic refrigeration system, resulting in a very useful tool for optimization of domestic refrigerators.

No description available.

The modelling of multi-phase water flow is an important modern-day design tool used by engineers to develop practical systems which are beneficial to society . Multi-phase water flow can be found in many important industrial applications such as large scale conventional and nuclear power systems, heat transfer machinery, chemical process plants, and other important examples. Because of many inherent complexities in physical two-phase flow processes, no generalised system of equations has been formulated that can accurately describe the two-phase flow of water at all flow conditions and system geometries. This has led to the development of many different models for the simulation of two-phase flow at specific conditions. These models vary greatly in complexity. The simplest model that can be used to simulate two-phase flow is termed the homogeneous equilibrium (HEM) two-phase flow model. This model has been found useful in investigations of choking and flashing flows, and as an initial investigative model used before the formulation of more complex models for specific applications. This flow model is fully de ned by three conservation equations, one each for mass, momentum and energy. To close the model, an equation of state (EOS) is required to deliver system pressure values. When solving the HEM, a general practice is to employ an equation of state that is derived from a fundamental expression of the second law of thermodynamics. This methodology has been proven to deliver accurate results for two-phase system simulations. This study focused on an alternative formulation of the equation of state which was previously developed for the time dependent modelling of HEM two-phase flow systems, termed the rate form of the equation of state (RFES). The goal of the study was not to develop a new formulation of the EOS, but rather to implement the RFES in a transient simulation model and to verify that this implementation delivers appropriate results when compared to the conventional implementation methodology. This was done by formulating a transient pipe and reservoir network model with the HEM, and closing the model using both the RFES and a benchmark EOS known to deliver accurate system property values. The results of the transient model simulations were then compared to determine whether the RFES delivered the expected results. It was found that the RFES delivered sufficiently accurate results for a variety of system transients, pressure conditions and numerical integration factors. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The modelling of multi-phase water flow is an important modern-day design tool used by engineers to develop practical systems which are beneficial to society . Multi-phase water flow can be found in many important industrial applications such as large scale conventional and nuclear power systems, heat transfer machinery, chemical process plants, and other important examples. Because of many inherent complexities in physical two-phase flow processes, no generalised system of equations has been formulated that can accurately describe the two-phase flow of water at all flow conditions and system geometries. This has led to the development of many different models for the simulation of two-phase flow at specific conditions. These models vary greatly in complexity. The simplest model that can be used to simulate two-phase flow is termed the homogeneous equilibrium (HEM) two-phase flow model. This model has been found useful in investigations of choking and flashing flows, and as an initial investigative model used before the formulation of more complex models for specific applications. This flow model is fully de ned by three conservation equations, one each for mass, momentum and energy. To close the model, an equation of state (EOS) is required to deliver system pressure values. When solving the HEM, a general practice is to employ an equation of state that is derived from a fundamental expression of the second law of thermodynamics. This methodology has been proven to deliver accurate results for two-phase system simulations. This study focused on an alternative formulation of the equation of state which was previously developed for the time dependent modelling of HEM two-phase flow systems, termed the rate form of the equation of state (RFES). The goal of the study was not to develop a new formulation of the EOS, but rather to implement the RFES in a transient simulation model and to verify that this implementation delivers appropriate results when compared to the conventional implementation methodology. This was done by formulating a transient pipe and reservoir network model with the HEM, and closing the model using both the RFES and a benchmark EOS known to deliver accurate system property values. The results of the transient model simulations were then compared to determine whether the RFES delivered the expected results. It was found that the RFES delivered sufficiently accurate results for a variety of system transients, pressure conditions and numerical integration factors. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014