Changes in the temporal variability of precipitation at all timescales are expected due to global warming. Such changes affect urban water infrastructure by potentially influencing their performance and risk of failure. Unfortunately, there is considerable uncertainty about how hydrological variables will change in the future. While uncertainty is present at all timescales, the climate signal in the daily time series simulated by climate models, for instance, can be estimated with much greater certainty than in the simulated hourly time series. That is problematic as sub-daily precipitation time series are essential to solving specific water resource engineering problems, especially in urban hydrology, where times of concentrations are typically less than a day. For instance, hourly or sub-hourly precipitation time series are routinely used to design stormwater and road drainage systems. Rainfall variability at sub-daily time steps is often represented as Intensity-Duration-Frequency (IDF) curves, relating precipitation duration (of basin time of concentration) to return period and average precipitation intensity. Naturally, several researchers investigated the integration of climate change in IDF curves, leading to methods of variable complexity and variable performance. This thesis aims to a) make a critical analysis of the most commonly used methods for IDF curves under climate change in Canada and b) identify the methods with optimal performance for a set of stations located in the South Nation watershed in Ottawa, Ontario, and c) perform a case study highlighting the effect of the choice of the temporal disaggregation method on the estimated risk of failure/performance of an urban water system. The first part of the thesis examines Equidistant Quantile Mapping (EQM) used in the IDF_CC tool developed for the Canadian Water Network project. Two conceptual flaws in the method that led to a systematic underestimation of extreme events were discovered. Two corrections are proposed to the EQM, leading to the development of two new methods for IDF generation. The output of EQM and its improved version is a time series of annual maximum precipitation intensity for different durations that can be used to derive IDF curves. These time series generated using the above approach are not appropriate for rainfall-runoff models for which continuous time series of precipitation (not only maximums) are required. The second part of the thesis tackles the issue, which examines a different approach to evaluating the risk of failure/performance of urban water systems under a changing climate. This second approach yields continuous time series of precipitation that can be fed in rainfall-runoff models used for IDF curve generation. The proposed method is applied in three steps: i) projections of future daily precipitation are generated by downscaling the output of climate models; ii) the downscaled daily precipitation time series are temporally disaggregated to an hourly time step using various techniques; iii) finally, the disaggregated future precipitation time series are used as inputs to rainfall-runoff models or used to generate IDF curves. This approach relaxes several strong assumptions made to develop the EQM approach, such as the implicit (and strong) assumption that the annual maximum precipitation at two different time steps occurs during the same event. That assumption is not necessarily valid and can affect the realism of the generated IDF curves. The method's performance is obviously dependent on the temporal disaggregation technique used in step 3. In this thesis, a simple steady-state stochastic disaggregation model that generates wet/dry day occurrence using a binomial distribution and precipitation intensity using an exponential distribution is proposed and compared to widely used temporal disaggregation methods: the multiplicative random cascade model (MRC), the Hurst-Kolmogorov process (HKP), and three versions of the K-nearest neighbor model (KNN) using the nonparametric Kolmogorov- Smirnov (KS) test. The six disaggregation techniques were assessed at four stations located in South Nation River Watershed located in Eastern Ontario, Canada. The third part of the thesis is a case study of the impact of climate change on stormwater management. First, a stormwater management model (SWMM) of St. Catharines, Ontario, developed in a previous study, was selected to simulate its stormwater and sanitary system. The model was forced with downscaled and temporally disaggregated precipitation outputs of the Canadian Regional Climate Model at the Port Dalhousie station, simulated under emission scenario RCP8.5. The temporal disaggregation was done using the Fahad-Ousmane and the KNN (30) methods developed in the previous chapter. The impact of climate change on the frequency, volume, and quality of combined sewer overflows and other hydraulic parameters is examined. Results suggest an increase in the total volume, flow frequency percentage, maximum flow, and average flow in the stormwater system due to climate change. Therefore, adaptation measures should be implemented for the distribution network and wastewater treatment plant to convey and treat the wastewater resulting from wet and dry events.

This thesis explores how to best choose data when curve fitting using power exponential functions. The power exponential functions used are μ(b; x)=(xe1-x)b and Φ(ρ; x)=((1-x)ex)ρ . We use a number of designs such as the equidistant design, the Chebyshev design and the the D-optimal design to compare which design gives the best fit. A few examples including the logistic and the heidler function are looked at during the comparison. The measurement of the errors were made based on the sum of least squares errors in the first part and the maximum error in the second part. MATLAB was used in this comparison.

Made available in DSpace on 2014-06-11T19:22:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-06-20Bitstream added on 2014-06-13T19:27:14Z : No. of bitstreams: 1 brachtvogel_el_me_botfca.pdf: 424866 bytes, checksum: 3ab3fe0b44645fcfe2ba5dd7b99a5f80 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A otimização da exploração dos recursos do ambiente é necessária para a maximização do rendimento do milho. Dentre os fatores que interferem na resposta ao ambiente está o arranjo de plantas, compreendido pelo arranjo espacial e área ocupada pela planta de milho, interagindo diretamente sobre a competição intraespecífica por fatores do meio. Desta forma, a hipótese desse trabalho é de que o arranjo espacial eqüidistante entre plantas de milho diminua os efeitos da competição intraespecífica principalmente em altas densidades, com conseqüente aumento da produtividade. Portanto, o objetivo deste trabalho é comparar as formas de distribuição espacial de plantas eqüidistante e o espaçamento de 0,80 metro na entrelinha, preconizado como o convencionalmente utilizado, em populações de 30000, 45000, 60000, 75000, 90000, 105000 plantas ha-1. O ensaio foi conduzido em área de Nitossolo Vermelho distroférrico, de textura argilosa situada na Fazenda Experimental Lageado, da Faculdade de Ciências Agronômicas da UNESP/Campus de Botucatu, na safra 2007/2008. O delineamento experimental foi o de blocos casualizados, em esquema fatorial 2 X 6 (quatro repetições), em parcelas de 4,5 x 10 metros. Foram avaliados altura das plantas, altura de inserção de espiga, relação entre altura da espiga e altura da planta e diâmetro do colmo em pleno florescimento; índice de área foliar no florescimento e na maturidade fisiológica, índice de persistência e senescência foliar, produção de massa de matéria seca por planta e por área no florescimento e na maturidade fisiológica, índice de remobilização, índice de colheita, comprimento de espiga, diâmetros de espiga e do sabugo, comprimento do grão, número de fileiras, massa de mil grãos, massa de grãos por espiga, índice de espiga, estimativa do número de espigas e grãos por hectare, população de plantas... / The maximization of environmental resources exploration is necessary to maximize maize grain yield. Among the factors that interfere in response to the environment is the plant arrangement, understood by spatial arrangement and occupied area by the maize plant, interacting on the intraspecific competition by factors of the environment. Thus, the hypothesis of this work is that the equidistant plant spacing between maize plants can reduce the effects of intraspecific competition mainly at high densities, aiming improvement of maize grain yield. The objective of this essay was to compare the equidistant plant spacing and 0.80 m row width, in populations of 30000, 45000, 60000, 75000, 90000, 105000 plants ha-1. The essay was located in a clay red alfisol area, in the Experimental Lageado Farm of the Agronomic Science College, UNESP-Botucatu-SP, in 2007/2008 growing season. The experimental design was a randomized block in four replications, in 4.5 x 10 m plots. It was evaluated plant and ear height, the relationship between ear and plant height and stem diameter at the flowering; leaf area index at the flowering and physiological maturity, leaf persistence and leaf senescence index, dry matter production per plant and per area at physiological maturity, steam remobilization index, harvest index, ear length, ear and cob diameter, grain length, number of grain rows, a thousand grains weight, grain weight per ear, ear index, ear and grain number per hectare, final plant population, percentage of stalk lodged plants, grain yield, as well the correlations between source and sink characteristics with yield. All parameters evaluated were affected by plant densities, except the mobilization and harvesting index. The spatial arrangements affected the relationship between ear and plant... (Complete abstract click electronic access below)

After the end of Cold War, China and ASEAN develop new international development strategies. China¡¦s new guiding principle of diplomacy is ¡§peace and development¡¨, and ASEAN hope to establish a multipolar world system through ¡§equidistant diplomacy¡¨ and regional economic integration. Due to the new international development strategies, China and ASEAN open the new cooperation opportunities, namely Mekong Subregion Cooperation, which concentrates on some functional sectors, such as transportation fundamental construction, investment, trade, agriculture and tourism sectors. With the effects of ¡§ramification¡¨, the functional cooperation is good in progress. This in turn pushes the interactions between China and ASEAN gradually ¡§spill-over¡¨ to political and security aspects which eventually make the ¡§East Asian Community¡¨ possible.

In computational finance, finite differences are a widely used tool in the valuation of standard derivative contracts. In a lower-dimensional setting, high accuracy and speed often characterize such methods, which gives them a competitive advantage against Monte Carlo methods. For option contracts with discontinuous payoff functions, however, finite differences encounter problems to maintain the order of convergence of the employed finite difference scheme. Therefore the timesteps are often computed in a conservative manner, which might increase the total execution time of the solver more than necessary.     It can be shown that for American call options written on dividend paying stocks, it may be optimal to exercise the option right before a dividend is paid out. The result is that yet another discontinuity is introduced in the solution and the timestep is often reduced to preserve the intrinsic convergence order. However, it is thought that at least in theory the optimal length of the timestep is an increasing function of the time elapsed since the last discontinuity occured. The objective thus becomes that of finding an explicit method for adjusting the timestep both at the dividend instants and between dividend instants. Keeping the discretization in space constant leads to a time non-equidistant finite difference problem.     The aim of this thesis is to propose a time non-equidistant numerical finite difference algorithm for valuation of American call options on stocks with dividends known in advance. In particular, an explicit formula is proposed for computing timesteps at the dividend instants and between dividend payments given a user-specified error tolerance. A portion of the report is also devoted to numerical stabilization techniques that are applied to maintain the convergence order, including Rannacher time-marching and mollification.

Orientador: Edson Agustini / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação / Made available in DSpace on 2018-08-11T06:10:14Z (GMT). No. of bitstreams: 1 Arcari_Inedio_M.pdf: 2739163 bytes, checksum: 0ea17bdba620035f3cb29f9033fab926 (MD5) Previous issue date: 2008 / Resumo: A presente dissertação é um texto introdutório de Geometria Hiperbólica com alguns resultados e comentários de Geometria Elíptica. Nossa intenção foi compilar um material que possa ser utilizado em cursos introdutórios de Geometria Hiperbólica tanto em nível de licenciatura quanto de bacharelado. Para tornar o texto mais acessível, notas históricas sobre a bela página do desenvolvimento das Geometrias Não Euclidianas foram introduzidas logo no primeiro capítulo. Procuramos ilustrar fartamente o texto com figuras dentre as quais várias que foram baseadas no Modelo Euclidiano do Disco de Poincaré para a Geometria Hiperbólica. Atualmente, o estudo de Geometria Hiperbólica tem sido bastante facilitado pelo uso de softwares de geometria dinâmica, como o Cabri-Géometre, GeoGebra e NonEuclid, sendo esses dois últimos softwares livres / Abstract: The present work is an introductory text of Hyperbolic Geometry with some results and comments of Elliptic eometry. Our aim in this work were to compile a material that can be used as introduction to Hyperbolic Geometry inundergraduated courses. In the first chapter we introduced historical notes about the beautiful development of the Non Euclid Geometries in order to turn the text more interesting and accesible. We illustrated the text with many figures which were done on the Euclidean Model of the Poincaré' s Disk for the Hyperbolic Geometry. In this way, the study of Hyperbolic Geometry has been softened by the use of softwares of dynamic geometry, like Cabri-Geométre and the freeware softwares GeoGebra and NonEuclid / Mestrado / Mestre em Matemática

Technological advancement such as the increase in processing power, hard disk capacity and network bandwidth has opened up many exciting new techniques to synthesise sounds, one of which is Concatenative Sound Synthesis (CSS). CSS uses data-driven method to synthesise new sounds from a large corpus of small sound snippets. This technique closely resembles the art of mosaicing, where small tiles are arranged together to create a larger image. A ‘target’ sound is often specified by users so that segments in the database that match those of the target sound can be identified and then concatenated together to generate the output sound. Whilst the practicality of CSS in synthesising sounds currently looks promising, there are still areas to be explored and improved, in particular the algorithm that is used to find the matching segments in the database. One of the main issues in CSS is the basis of similarity, as there are many perceptual attributes which sound similarity can be based on, for example it can be based on timbre, loudness, rhythm, and tempo and so on. An ideal CSS system needs to be able to decipher which of these perceptual attributes are anticipated by the users and then accommodate them by synthesising sounds that are similar with respect to the particular attribute. Failure to communicate the basis of sound similarity between the user and the CSS system generally results in output that mismatches the sound which has been envisioned by the user. In order to understand how humans perceive sound similarity, several elements that affected sound similarity judgment were first investigated. Of the four elements tested (timbre, melody, loudness, tempo), it was found that the basis of similarity is dependent on humans’ musical training where musicians based similarity on the timbral information, whilst non-musicians rely on melodic information. Thus, for the rest of the study, only features that represent the timbral information were included, as musicians are the target user for the findings of this study. Another issue with the current state of CSS systems is the user control flexibility, in particular during segment matching, where features can be assigned with different weights depending on their importance to the search. Typically, the weights (in some existing CSS systems that support the weight assigning mechanism) can only be assigned manually, resulting in a process that is both labour intensive and time consuming. Additionally, another problem was identified in this study, which is the lack of mechanism to handle homosonic and equidistant segments. These conditions arise when too few features are compared causing otherwise aurally different sounds to be represented by the same sonic values, or can also be a result of rounding off the values of the features extracted. This study addresses both of these problems through an extended use of Artificial Intelligence (AI). The Analysis Hierarchy Process (AHP) is employed to enable order dependent features selection, allowing weights to be assigned for each audio feature according to their relative importance. Concatenation distance is used to overcome the issues with homosonic and equidistant sound segments. The inclusion of AI results in a more intelligent system that can better handle tedious tasks and minimize human error, allowing users (composers) to worry less of the mundane tasks, and focusing more on the creative aspects of music making. In addition to the above, this study also aims to enhance user control flexibility in a CSS system and improve similarity result. The key factors that affect the synthesis results of CSS were first identified and then included as parametric options which users can control in order to communicate their intended creations to the system to synthesise. Comprehensive evaluations were carried out to validate the feasibility and effectiveness of the proposed solutions (timbral-based features set, AHP, and concatenation distance). The final part of the study investigates the relationship between perceived sound similarity and perceived sound interestingness. A new framework that integrates all these solutions, the query-based CSS framework, was then proposed. The proof-of-concept of this study, ConQuer, was developed based on this framework. This study has critically analysed the problems in existing CSS systems. Novel solutions have been proposed to overcome them and their effectiveness has been tested and discussed, and these are also the main contributions of this study.

Orientador: Silvio José Bicudo / Banca: Claudio Cavariani / Banca: Augusto Dias kanthack / Resumo: A otimização da exploração dos recursos do ambiente é necessária para a maximização do rendimento do milho. Dentre os fatores que interferem na resposta ao ambiente está o arranjo de plantas, compreendido pelo arranjo espacial e área ocupada pela planta de milho, interagindo diretamente sobre a competição intraespecífica por fatores do meio. Desta forma, a hipótese desse trabalho é de que o arranjo espacial eqüidistante entre plantas de milho diminua os efeitos da competição intraespecífica principalmente em altas densidades, com conseqüente aumento da produtividade. Portanto, o objetivo deste trabalho é comparar as formas de distribuição espacial de plantas eqüidistante e o espaçamento de 0,80 metro na entrelinha, preconizado como o convencionalmente utilizado, em populações de 30000, 45000, 60000, 75000, 90000, 105000 plantas ha-1. O ensaio foi conduzido em área de Nitossolo Vermelho distroférrico, de textura argilosa situada na Fazenda Experimental Lageado, da Faculdade de Ciências Agronômicas da UNESP/Campus de Botucatu, na safra 2007/2008. O delineamento experimental foi o de blocos casualizados, em esquema fatorial 2 X 6 (quatro repetições), em parcelas de 4,5 x 10 metros. Foram avaliados altura das plantas, altura de inserção de espiga, relação entre altura da espiga e altura da planta e diâmetro do colmo em pleno florescimento; índice de área foliar no florescimento e na maturidade fisiológica, índice de persistência e senescência foliar, produção de massa de matéria seca por planta e por área no florescimento e na maturidade fisiológica, índice de remobilização, índice de colheita, comprimento de espiga, diâmetros de espiga e do sabugo, comprimento do grão, número de fileiras, massa de mil grãos, massa de grãos por espiga, índice de espiga, estimativa do número de espigas e grãos por hectare, população de plantas... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The maximization of environmental resources exploration is necessary to maximize maize grain yield. Among the factors that interfere in response to the environment is the plant arrangement, understood by spatial arrangement and occupied area by the maize plant, interacting on the intraspecific competition by factors of the environment. Thus, the hypothesis of this work is that the equidistant plant spacing between maize plants can reduce the effects of intraspecific competition mainly at high densities, aiming improvement of maize grain yield. The objective of this essay was to compare the equidistant plant spacing and 0.80 m row width, in populations of 30000, 45000, 60000, 75000, 90000, 105000 plants ha-1. The essay was located in a clay red alfisol area, in the Experimental Lageado Farm of the Agronomic Science College, UNESP-Botucatu-SP, in 2007/2008 growing season. The experimental design was a randomized block in four replications, in 4.5 x 10 m plots. It was evaluated plant and ear height, the relationship between ear and plant height and stem diameter at the flowering; leaf area index at the flowering and physiological maturity, leaf persistence and leaf senescence index, dry matter production per plant and per area at physiological maturity, steam remobilization index, harvest index, ear length, ear and cob diameter, grain length, number of grain rows, a thousand grains weight, grain weight per ear, ear index, ear and grain number per hectare, final plant population, percentage of stalk lodged plants, grain yield, as well the correlations between source and sink characteristics with yield. All parameters evaluated were affected by plant densities, except the mobilization and harvesting index. The spatial arrangements affected the relationship between ear and plant... (Complete abstract click electronic access below) / Mestre

An AC system’s voltage unbalance by a fundamental frequency negative sequence system is usually the main cause for the emission of non-characteristic harmonics by current source converters as used in conventional HVDC systems. This emission takes place on both sides of each 12-pulse converter. On the DC side mainly a 2nd harmonic voltage appears driving a 2nd harmonic current. The magnitude of this harmonic current can exceed the magnitudes of the characteristic harmonics even if no low order resonance exists. Further non-characteristic harmonics generated by the converter under such unbalanced supply voltage conditions have frequencies with a frequency distance to the characteristic harmonics of 2 times the fundamental frequency. The main technical drawbacks are the unintended coupling between both AC systems and the risk of thyristor over-stresses by DC current discontinuities at low power transfer levels. On both AC sides the largest 2 non-characteristic current harmonics generated by a 12-pulse HVDC converter under unbalanced supply voltage conditions are a negative sequence system of the fundamental harmonic and a positive sequence system of the 3rd harmonic. Also on the AC sides further harmonics are emitted by the converter with a order number distance of 2 to the orders of the characteristic harmonics. However, in practical AC system operation special attention has to be paid to the 3rd harmonic distortion level, in particular when low order resonance appears between the system impedance and the impedance of the converter station AC filters. In order to avoid the above mentioned problems, large smoothing reactors and sometimes large blocking filters are installed on the DC side and the voltage distortion on the AC sides is reduced by AC filters. However, these filters require an expensive high component rating if they are tuned to the 2nd or 3rd harmonic respectively. The work shows that a modification of the valve firing can reduce the levels of the 2nd and 3rd harmonic without investment into additional primary equipment. Furthermore, this offers the chance to reduce the minimum power transfer level since also the risk of an intermittent DC current can be reduced. A corresponding algorithm and a control strategy are proposed. However, the calculation of an appropriate firing pattern requires a detailed modelling of the processes within the converters, especially the formation of the harmonics and the harmonic transfer between AC and DC sides. The work proposes a component vector model for the calculation of the harmonics. This model assumes that each harmonic consists of a first component representing the ideal conversion process, a 2nd component representing the impact of different commutation angles and in the case of the modified firing a 3rd component considering the impact of the intended non-equidistant firing. The work shows, that the harmonic component vectors resulting from voltage unbalance and from firing modulation can be treated separately and superimposed linearly. The calculation of the harmonic component vectors is performed applying the method of switching functions. For the consideration of the commutation and firing angle differences the modelling of switching functions based on differential impulses is proposed. However, especially an accurate representation of the above mentioned 2nd component vector requires a correct calculation of the commutation angles and their valve-specific differences. The investigations of this work have revealed that the conventional method of calculating the commutation angles – assuming an ideal smoothed DC current - may not produce results of sufficient accuracy. This is especially true in the case of a high ripple of the DC current, e.g. smoothed with a small smoothing reactor. A small smoothing reactor is typical for HVDC back-to-back applications. Therefore a new analytical method for the calculation of the commutation angles has been developed which in particular considers the typical pulse form of the DC current and additionally the impacts of the voltage unbalance and of the proposed modification of the firing on the ripple shape of the DC current. Moreover, as this analytical method requires the instantaneous values of the DC current at the instants of valve firing, a further analytical method for the calculation of these discrete current values has been developed. The equations are valid under the same conditions as the new ones for calculation of the commutation angles, i.e. resistive-inductive AC system fundamental frequency impedances, any degree of DC current smoothing between ideal smoothing and a ripple at the limit for current discontinuities. Symmetrical conditions, supply voltage unbalances and non-equidistant firing as proposed are applied. It is shown that, using this method, also the discrete values of the DC current at the end of the commutation intervals can be determined. In practice one of these discrete current values indicates the minimum value during one period of the fundamental frequency. This offers the chance for a more exact analytical determination of the limit for the appearance of DC current discontinuities. For typical parameters of a back-to-back installation the new methods and the new analytical equations have been compared with simulation results showing excellent correlation for typical voltage unbalances of not more than 1...2% and firing angle differences of not more than 2.5°. This verification is performed for the harmonics, the commutation angles and the discrete values of the DC current at the firing instants as well.

An AC system’s voltage unbalance by a fundamental frequency negative sequence system is usually the main cause for the emission of non-characteristic harmonics by current source converters as used in conventional HVDC systems. This emission takes place on both sides of each 12-pulse converter. On the DC side mainly a 2nd harmonic voltage appears driving a 2nd harmonic current. The magnitude of this harmonic current can exceed the magnitudes of the characteristic harmonics even if no low order resonance exists. Further non-characteristic harmonics generated by the converter under such unbalanced supply voltage conditions have frequencies with a frequency distance to the characteristic harmonics of 2 times the fundamental frequency. The main technical drawbacks are the unintended coupling between both AC systems and the risk of thyristor over-stresses by DC current discontinuities at low power transfer levels. On both AC sides the largest 2 non-characteristic current harmonics generated by a 12-pulse HVDC converter under unbalanced supply voltage conditions are a negative sequence system of the fundamental harmonic and a positive sequence system of the 3rd harmonic. Also on the AC sides further harmonics are emitted by the converter with a order number distance of 2 to the orders of the characteristic harmonics. However, in practical AC system operation special attention has to be paid to the 3rd harmonic distortion level, in particular when low order resonance appears between the system impedance and the impedance of the converter station AC filters. In order to avoid the above mentioned problems, large smoothing reactors and sometimes large blocking filters are installed on the DC side and the voltage distortion on the AC sides is reduced by AC filters. However, these filters require an expensive high component rating if they are tuned to the 2nd or 3rd harmonic respectively. The work shows that a modification of the valve firing can reduce the levels of the 2nd and 3rd harmonic without investment into additional primary equipment. Furthermore, this offers the chance to reduce the minimum power transfer level since also the risk of an intermittent DC current can be reduced. A corresponding algorithm and a control strategy are proposed. However, the calculation of an appropriate firing pattern requires a detailed modelling of the processes within the converters, especially the formation of the harmonics and the harmonic transfer between AC and DC sides. The work proposes a component vector model for the calculation of the harmonics. This model assumes that each harmonic consists of a first component representing the ideal conversion process, a 2nd component representing the impact of different commutation angles and in the case of the modified firing a 3rd component considering the impact of the intended non-equidistant firing. The work shows, that the harmonic component vectors resulting from voltage unbalance and from firing modulation can be treated separately and superimposed linearly. The calculation of the harmonic component vectors is performed applying the method of switching functions. For the consideration of the commutation and firing angle differences the modelling of switching functions based on differential impulses is proposed. However, especially an accurate representation of the above mentioned 2nd component vector requires a correct calculation of the commutation angles and their valve-specific differences. The investigations of this work have revealed that the conventional method of calculating the commutation angles – assuming an ideal smoothed DC current - may not produce results of sufficient accuracy. This is especially true in the case of a high ripple of the DC current, e.g. smoothed with a small smoothing reactor. A small smoothing reactor is typical for HVDC back-to-back applications. Therefore a new analytical method for the calculation of the commutation angles has been developed which in particular considers the typical pulse form of the DC current and additionally the impacts of the voltage unbalance and of the proposed modification of the firing on the ripple shape of the DC current. Moreover, as this analytical method requires the instantaneous values of the DC current at the instants of valve firing, a further analytical method for the calculation of these discrete current values has been developed. The equations are valid under the same conditions as the new ones for calculation of the commutation angles, i.e. resistive-inductive AC system fundamental frequency impedances, any degree of DC current smoothing between ideal smoothing and a ripple at the limit for current discontinuities. Symmetrical conditions, supply voltage unbalances and non-equidistant firing as proposed are applied. It is shown that, using this method, also the discrete values of the DC current at the end of the commutation intervals can be determined. In practice one of these discrete current values indicates the minimum value during one period of the fundamental frequency. This offers the chance for a more exact analytical determination of the limit for the appearance of DC current discontinuities. For typical parameters of a back-to-back installation the new methods and the new analytical equations have been compared with simulation results showing excellent correlation for typical voltage unbalances of not more than 1...2% and firing angle differences of not more than 2.5°. This verification is performed for the harmonics, the commutation angles and the discrete values of the DC current at the firing instants as well.:1 Einleitung und Ziel der Arbeit 1.1 Einführung in die Problematik 1.2 HGÜ-Systeme als Quelle von Strom- und Spannungsharmonischen 1.3 Netzspannungsunsymmetrien 1.4 Abgrenzung der betrachteten technischen Systeme 1.5 Beweggründe für die Betrachtung 1.6 Zielstellungen 2 Erkenntnisstand und Analyse der Aufgabenstellung 2.1 Harmonische 2.2 Aktive Kompensation von Harmonischen 2.3 Diskrete Werte des Zwischenkreisstromes am Beginn und Ende der Kommutierungsintervalle 2.4 Kommutierungswinkel 3 Grundlagen 3.1 Methodischer Ansatz 3.2 Allgemeine Voraussetzungen, Annahmen und Festlegungen 3.3 Maßgebliche Impedanzen für die Stromaufteilung 3.4 Maßgebliche Impedanz für die gleichstromseitigen Stromharmonischen 3.5 Leerlauf-Klemmenspannung des Stromrichters 3.6 Kommutierungsspannung 3.7 Nummerierungssystem der Ventile 3.8 Überlappungsformen der Kommutierungsintervalle 3.9 Komplexer Spannungsunsymmetriefaktor 3.10 Anwendung und Modifikation von Schaltfunktionen 3.11 Verifikation der Ergebnisse 4 Harmonische auf der Gleichstromseite 4.1 Bildungsgesetz 4.2 Charakteristische Harmonische 4.3 Nichtcharakteristische Harmonische infolge unsymmetrischer Netzspannungen 4.4 Nichtcharakteristische Harmonische infolge Ansteuermodifikation 5 Diskreter Wert des Zwischenkreisstromes im Zündzeitpunkt 5.1 Vorgehensweise 5.2 Lösungsansatz 5.3 Konstante Gegenspannung 5.4 Reale Gegenspannung des HGÜ-Stromrichters 5.5 Berücksichtigung von Resistanzen 5.6 Unsymmetrische Netzspannungen 5.7 Ansteuermodifikation 5.8 Unsymmetrische Netzspannungen und gleichzeitige Ansteuermodifikation 5.9 Ergebnisse 6 Kommutierungswinkel 6.1 Vorgehensweise 6.2 Konstante Gegenspannung 6.3 Reale Gegenspannung des HGÜ-Stromrichters 6.4 Berücksichtigung von Resistanzen 6.5 Unsymmetrische Netzspannungen 6.6 Ansteuermodifikation 6.7 Unsymmetrische Netzspannungen und gleichzeitige Ansteuermodifikation 6.8 Ergebnisse 7 Vertiefende Betrachtung der nichtcharakteristischen Harmonischen auf der Gleichstromseite 7.1 Vorbemerkungen 7.2 Unsymmetrische Netzspannungen 7.3 Ansteuermodifikation 7.4 Spannungsunsymmetrie und gleichzeitige Ansteuermodifikation 7.5 Ergebnisse 8 Harmonische auf der Netzseite 8.1 Bildungsgesetz 8.2 Charakteristische Harmonische 8.3 Nichtcharakteristische Harmonische 9 Betrachtungen zur aktiven Kompensation 9.1 Vorbemerkungen 9.2 Betrachtungsumfang 9.3 Grundlagen 9.4 Konzeptioneller Vorschlag für die Kompensation der 2. Stromharmonischen 9.5 Betrachtung der Drehstromseite 9.6 Vorschlag zur Weiterentwicklung des Konzeptes 9.7 Berechnungsbeispiel zur Kompensation der 2. Harmonischen im Zwischenkreis 9.8 Ergebnisse und Schlussfolgerungen 10 Zusammenfassung 11 Literatur 12 Formelzeichen und Abkürzungen 13 Anlagenverzeichnis