SuperNEC is a method of moments (MoM) electromagnetic eld solver based on the Numerical Electromagnetics Code (NEC). Much of the simulation time can be attributed to the lling of the impedance matrix, which is performed at each frequency point of interest. Impedance matrix interpolation methods have been implemented in SuperNEC to reduce the computational time required to ll the impedance matrix [Z]. Elements in [Z] vary predictably over frequency and can be approximated by a second order polynomial. A second improved method is implemented where the dominant frequency variation term is removed prior to calculating the tting function. A method of determining the optimum sample range relative to simulation range and maximum interaction distance has been developed. Given the correct choice of sample range the mean error in the MoM solution is less than 10% over the frequency range and the input impedance can be reproduced with good agreement over a wide bandwith. Improvement in the simulation e ciency of 1.7 times can be expected if su cient frequency points are of interest to account for the computational time required to sample the matrix and determine tting function coe cients. This method has been applied to a dipole antenna, an LPDA and a horn antenna. To increase the simulation bandwidth and retain an acceptable level of accuracy, the bandwidth is split into multiple sub-bands.

Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion. A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated. Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods. One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems. In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.

Power system faults normally result in system damage, profit loss and consumer dissatisfaction. Consequently, there is a strong demand on precise and fast fault location estimation for power system to minimize the system restoration time. This paper examines a method to locate short-circuit faults on a distribution system with unbalanced loads without fault type information. Bus impedance matrix technique was harnessed in the fault location estimation algorithm. The system data including line impedances, source impedance and distribution system layout was assumed to be known factors, hence pre-fault bus impedance can be calculated and implemented into the algorithm. Corresponding methods to derive system matrix information were discussed. Case studies were performed to evaluate the accuracy of the fault location algorithm and illustrate the robust performance under measurements errors influences, load variation impacts and load compensation implementations. Traditional fault location methods involve current and voltage measurements mandatorily locating at each ends of faulted section to locate the fault. The method examined finds fault location for distribution system utilizing impedance matrix accompanied with sparse measurements in the power network. This method fully considers the unbalance of distribution system.

In modern power transmission systems, the double-circuit line structure is increasingly adopted. However, due to the mutual coupling between the parallel lines it is quite challenging to design accurate fault location algorithms. Moreover, the widely used series compensator and its protective device introduce harmonics and non-linearities to the transmission lines, which make fault location more difficult. To tackle these problems, this dissertation is committed to developing advanced fault location methods for double-circuit and series-compensated transmission lines. Algorithms utilizing sparse measurements for pinpointing the location of short-circuit faults on double-circuit lines are proposed. By decomposing the original network into three sequence networks, the bus impedance matrix for each network with the addition of the fictitious fault bus can be formulated. It is a function of the unknown fault location. With the augmented bus impedance matrices the sequence voltage change during the fault at any bus can be expressed in terms of the corresponding sequence fault current and the transfer impedance between the fault bus and the measured bus. Resorting to VCR the superimposed sequence current at any branch can be expressed with respect to the pertaining sequence fault current and transfer impedance terms. Obeying boundary conditions of different fault types, four different classes of fault location algorithms utilizing either voltage phasors, or phase voltage magnitudes, or current phasors, or phase current magnitudes are derived. The distinguishing charactristic of the proposed method is that the data measurements need not stem from the faulted section itself. Quite satisfactory results have been obtained using EMTP simulation studies. A fault location algorithm for series-compensated transmission lines that employs two-terminal unsynchronized voltage and current measurements has been implemented. For the distinct cases that the fault occurs either on the left or on the right side of the series compensator, two subroutines are developed. In additon, the procedure to identify the correct fault location estimate is described in this work. Simulation studies carried out with Matlab SimPowerSystems show that the fault location results are very accurate.

Nesta dissertação, é apresentada uma metodologia para cálculo de afundamentos de tensão na presença de fontes alternativas de energia. Um método para determinar o grau de influência da reatância de outras unidades geradoras conectadas ao sistema elétrico no que se refere a afundamentos de tensão é desenvolvido. É utilizada a matriz impedância de barras – Zbus para a obtenção de expressões analíticas para a magnitude de afundamentos de tensão causados por faltas na rede. Uma análise matemática das expressões obtidas e uma análise de sensibilidade são feitas com observações acerca das características propiciadas pela inserção de novas fontes de geração. As expressões analíticas são utilizadas para classificar as barras quanto ao número de afundamentos causados por faltas trifásicas e fase-terra em todas as barras do sistema. De maneira similar, a alocação de uma unidade de geração específica é feita com o objetivo de reduzir o número de afundamentos de tensão observados na rede. As expressões em termos da reatância do gerador são usadas na solução de um conjunto de inequações observando a necessidade da manutenção de níveis mínimos aceitáveis de tensão requisitados por cargas sensíveis, a relação entre a reatância do novo gerador e sua capacidade de mitigação de afundamentos fica evidenciada. / This work presents a methodology for voltage sags analysis in the presence of alternative energy sources. The method determines the degree of influence of the reactance from the new generating units connected to the electrical system with regard to voltage sags magnitudes. The impedance matrix – Zbus is used to obtain analytical expressions voltage sags magnitude caused by faults in the grid. A mathematical analysis of the obtained expressions and a sensitivity analysis are made with observations about the characteristics afforded by the inclusion of new generation sources. The analytical expressions are used to rank the bars as the number of sags caused by three-phase and phase to ground faults on all system buses. Similarly, the allocation of a specific generation unit is done in order to reduce the number of voltage sags over the grid. The expressions in terms of the generator reactance are used on solving a set of inequalities, observing the need to maintain minimum acceptable voltage levels required by sensitive loads, the relationship between the reactance of the new generator and its sag mitigation capability is evidenced.

Nesta dissertação, é apresentada uma metodologia para cálculo de afundamentos de tensão na presença de fontes alternativas de energia. Um método para determinar o grau de influência da reatância de outras unidades geradoras conectadas ao sistema elétrico no que se refere a afundamentos de tensão é desenvolvido. É utilizada a matriz impedância de barras – Zbus para a obtenção de expressões analíticas para a magnitude de afundamentos de tensão causados por faltas na rede. Uma análise matemática das expressões obtidas e uma análise de sensibilidade são feitas com observações acerca das características propiciadas pela inserção de novas fontes de geração. As expressões analíticas são utilizadas para classificar as barras quanto ao número de afundamentos causados por faltas trifásicas e fase-terra em todas as barras do sistema. De maneira similar, a alocação de uma unidade de geração específica é feita com o objetivo de reduzir o número de afundamentos de tensão observados na rede. As expressões em termos da reatância do gerador são usadas na solução de um conjunto de inequações observando a necessidade da manutenção de níveis mínimos aceitáveis de tensão requisitados por cargas sensíveis, a relação entre a reatância do novo gerador e sua capacidade de mitigação de afundamentos fica evidenciada. / This work presents a methodology for voltage sags analysis in the presence of alternative energy sources. The method determines the degree of influence of the reactance from the new generating units connected to the electrical system with regard to voltage sags magnitudes. The impedance matrix – Zbus is used to obtain analytical expressions voltage sags magnitude caused by faults in the grid. A mathematical analysis of the obtained expressions and a sensitivity analysis are made with observations about the characteristics afforded by the inclusion of new generation sources. The analytical expressions are used to rank the bars as the number of sags caused by three-phase and phase to ground faults on all system buses. Similarly, the allocation of a specific generation unit is done in order to reduce the number of voltage sags over the grid. The expressions in terms of the generator reactance are used on solving a set of inequalities, observing the need to maintain minimum acceptable voltage levels required by sensitive loads, the relationship between the reactance of the new generator and its sag mitigation capability is evidenced.

Nesta dissertação, é apresentada uma metodologia para cálculo de afundamentos de tensão na presença de fontes alternativas de energia. Um método para determinar o grau de influência da reatância de outras unidades geradoras conectadas ao sistema elétrico no que se refere a afundamentos de tensão é desenvolvido. É utilizada a matriz impedância de barras – Zbus para a obtenção de expressões analíticas para a magnitude de afundamentos de tensão causados por faltas na rede. Uma análise matemática das expressões obtidas e uma análise de sensibilidade são feitas com observações acerca das características propiciadas pela inserção de novas fontes de geração. As expressões analíticas são utilizadas para classificar as barras quanto ao número de afundamentos causados por faltas trifásicas e fase-terra em todas as barras do sistema. De maneira similar, a alocação de uma unidade de geração específica é feita com o objetivo de reduzir o número de afundamentos de tensão observados na rede. As expressões em termos da reatância do gerador são usadas na solução de um conjunto de inequações observando a necessidade da manutenção de níveis mínimos aceitáveis de tensão requisitados por cargas sensíveis, a relação entre a reatância do novo gerador e sua capacidade de mitigação de afundamentos fica evidenciada. / This work presents a methodology for voltage sags analysis in the presence of alternative energy sources. The method determines the degree of influence of the reactance from the new generating units connected to the electrical system with regard to voltage sags magnitudes. The impedance matrix – Zbus is used to obtain analytical expressions voltage sags magnitude caused by faults in the grid. A mathematical analysis of the obtained expressions and a sensitivity analysis are made with observations about the characteristics afforded by the inclusion of new generation sources. The analytical expressions are used to rank the bars as the number of sags caused by three-phase and phase to ground faults on all system buses. Similarly, the allocation of a specific generation unit is done in order to reduce the number of voltage sags over the grid. The expressions in terms of the generator reactance are used on solving a set of inequalities, observing the need to maintain minimum acceptable voltage levels required by sensitive loads, the relationship between the reactance of the new generator and its sag mitigation capability is evidenced.

El Método de los Momentos (MoM) ha sido ampliamente utilizado en las últimas décadas para la discretización y la solución de las formulaciones de ecuación integral que aparecen en muchos problemas electromagnéticos de antenas y dispersión. Las más utilizadas de dichas formulaciones son la Ecuación Integral de Campo Eléctrico (EFIE), la Ecuación Integral de Campo Magnético (MFIE) y la Ecuación Integral de Campo Combinada (CFIE), que no es más que una combinación lineal de las dos anteriores.Las formulaciones MFIE y CFIE son válidas únicamente para objetos cerrados y necesitan tratar la integración de núcleos con singularidades de orden superior al de la EFIE. La falta de técnicas eficientes y precisas para el cálculo de dichas integrales singulares a llevado a imprecisiones en los resultados. Consecuentemente, su uso se ha visto restringido a propósitos puramente académicos, incluso cuando tienen una velocidad de convergencia muy superior cuando son resuelto iterativamente, debido a su excelente número de condicionamiento.En general, la principal desventaja del MoM es el alto coste de su construcción, almacenamiento y solución teniendo en cuenta que es inevitablemente un sistema denso, que crece con el tamaño eléctrico del objeto a analizar. Por tanto, un gran número de métodos han sido desarrollados para su compresión y solución. Sin embargo, muchos de ellos son absolutamente dependientes del núcleo de la ecuación integral, necesitando de una reformulación completa para cada núcleo, en caso de que sea posible.Esta tesis presenta nuevos enfoques o métodos para acelerar y incrementar la precisión de ecuaciones integrales discretizadas con el Método de los Momentos (MoM) en electromagnetismo computacional.En primer lugar, un nuevo método iterativo rápido, el Multilevel Adaptive Cross Approximation (MLACA), ha sido desarrollado para acelerar la solución del sistema lineal del MoM. En la búsqueda por un esquema de propósito general, el MLACA es un método independiente del núcleo de la ecuación integral y es puramente algebraico. Mejora simultáneamente la eficiencia y la compresión con respecto a su versión mono-nivel, el ACA, ya existente. Por tanto, representa una excelente alternativa para la solución del sistema del MoM de problemas electromagnéticos de gran escala.En segundo lugar, el Direct Evaluation Method, que ha provado ser la referencia principal en términos de eficiencia y precisión, es extendido para superar el cálculo del desafío que suponen las integrales hiper-singulares 4-D que aparecen en la formulación de Ecuación Integral de Campo Magnético (MFIE) así como en la de Ecuación Integral de Campo Combinada (CFIE). La máxima precisión asequible -precisión de máquina se obtiene en un tiempo más que razonable, sobrepasando a cualquier otra técnica existente en la bibliografía.En tercer lugar, las integrales hiper-singulares mencionadas anteriormente se convierten en casi-singulares cuando los elementos discretizados están muy próximo pero sin llegar a tocarse. Se muestra como las reglas de integración tradicionales tampoco convergen adecuadamente en este caso y se propone una posible solución, basada en reglas de integración más sofisticadas, como la Double Exponential y la Gauss-Laguerre.Finalmente, un esfuerzo en facilitar el uso de cualquier programa de simulación de antenas basado en el MoM ha llevado al desarrollo de un modelo matemático general de un puerto de excitación en el espacio discretizado. Con este nuevo modelo, ya no es necesaria la adaptación de los lados del mallado al puerto en cuestión. / The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy --machine precision-- is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the usability of any antenna simulation software based on the MoM has led to the development of a general mathematical model of an excitation port in the discretized space. With this new model, it is no longer necessary to adapt the mesh edges to the port.

This thesis introduces efficient numerical techniques for the analysis of novel electromagnetic metamaterials. The modelling is based on a Method of Moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. Triangular basis functions are used that allow for modelling of arbitrary shaped metallic elements. Unlike the conventional methods, impedance interpolation is applied to derive the dispersion characteristics of planar periodic structures. With these techniques, the plane wave and the surface wave responses of fractal structures have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structures are presented. Based on this method, novel planar left-handed metamaterials are also proposed. Verifications of the left-handedness are presented by means of full wave simulation of finite planar arrays using commercial software and lab measurement. The structures are simple, readily scalable to higher frequencies and compatible with low-cost fabrication techniques.

This work deals with the method for analysis of one-port microstrip circuits which is called as contour-integral method. The general procedure for evaluating of important parameters concerning the analysis of microstrip antennas is given. Next, the geometrical parameters necessary for the calculation of elements in U and H matrices are numerically solved. With the help of these matrices, the input impedance or the reflection coefficient can be easily found.