Parts of the auxiliary power systems at Fortum's hydro power stations are usingdirect current, which is fed from the generators at the plant and converted byrectifiers. As photovoltaic solar cells produce direct current there are severalhypothetical advantages to use solar power for the auxiliary power supply, e.g.enabling more of the power from the generator to be sold to the grid. It eliminatesthe need of an inverter, conversion losses are avoided and less load is put on therectifiers. However the exclusion of an inverter also prevents the solar cells to have adirect connection to the grid, which in turn makes them ineligible for the Swedishgovernmental solar power investment support program. The lesser load on therectifiers will not affect their lifetime according to manufacturers and thus achieves noeconomic gain. Avoiding conversion losses will increase the gain from the producedelectricity by enabling even more power to be sold to the grid. The economic gainfrom avoiding conversion losses is however too small to gain any feasibility in a smallsolar power installation at a hydro power plant, as the small size will make itexpensive in terms of investment per Wp.

In this thesis, a simple model of the stretched magnetic field lines in the nightside magnetotail was created. The nightside magnetosphere model contains four main regions: plasmasphere, plasma sheet, magnetic lobes, and low latitude boundary layers. The plasma sheet is split into three regions based on the shape of the closed field lines present: dipole plasma sheet, transition plasma sheet, and stretched plasma sheet (SPS). The SPS, the focus of this thesis, is split into two regions: disruption zones (DZs) and a central neutral sheet (NS). The shape of the stretched field lines contain four inflection points. The convex curvature regions form the DZs and the central concave curvature region forms the NS. The NS is split into two regions: outer neutral sheet (ONS) and inner neutral sheet (INS). Due to the reversal of the x-component of the magnetic field at the center line of the NS, the protons are magnetized in the ONS and "unmagnetized" in the INS. There are two main current systems in the SPS. The first is a double vortex current system consisting of eastward current in the DZs that closes westward in the NS. The second system is the NS field-aligned current (FAC) system. It is generated in the INS mainly by the earthward convective drift of the electrons while the "unmagnetized" protons have little convective drift and remain tailward of the electrons. This FAC system produces the pre-onset electron auroral arc during the growth phase of the substorm. A simple model of the stretched magnetic field lines was created in order to calculate the current systems present in the SPS. The simple model was based entirely upon the shape of the stretched field lines. It passed two physical tests, divergence of the magnetic field and limits at infinity, so it was used to calculate currents. The total current using Ampere's law and the curvature current was found. Both results agreed with the double vortex current system.

Confined coasts in general, and pocket beach environments in particular, are under huge development pressures worldwide, not least due to their sheltered nature and perceived shoreline stability. However, understanding of their physical functioning is poor in comparison to that of open coast beaches. This study aims to improve understanding in terms of the existing gaps in knowledge of wave processes and nearshore currents, and also to examine the importance of local wind and tide factors in generating nearshore currents, in micro-tidal pocket beaches. The boundaries of embayments are generally recognized as important controls of their beach processes and responses, yet little detailed knowledge exists of how the exact embayment dimensions and characteristics influences these processes. One key embayment feature the influence of which is poorly understood is the downcoast headland. In this thesis, field observations plus Zanuttigh and Van der Meer’s (2008) approach, and the SWAN wave model were used to evaluate the downcoast headland effects on wave processes within Okains Bay, an example pocket beach environment. The results showed that incident wave heights and directions were significantly influenced by wave reflection processes from the downcoast headland inside the bay. The intensity of reflection effects on wave characteristics inside the pocket beach varied according to approaching wave direction. Reflection effects reduced when waves approached from angles close to parallel to the headlands, increasing towards headland-perpendicular wave approaches. Field observations and the XBeach model were used to examine whether or not tides can significantly influence nearshore currents within example and model pocket beach environments. Results indicated that tides can be the primary driver of nearshore currents close to the bed inside micro-tidal pocket beaches, depending on incident wave conditions. In areas of micro-tidal pocket beaches exposed to direct approaching waves, currents were wave driven, while in areas further into the bay that experienced headland filtering of their wave environment, currents were mainly tide generated. The results of this study demonstrated how the current circulation system within micro-tidal pocket beaches is related to the incoming directions of offshore waves. If high energy waves approach oblique or normal to the shoreline (with the assumption that the shoreline is at 90° to the headlands), the current system was found to consist of longshore currents influenced by headlands, plus a rip current in the center of the shoreline or a toporip in proximity to headlands. The location of the rip current or toporip was determined by the direction of approaching incident waves. This study also examined the behavior of local winds in a pocket beach environment and their consequent effects on nearshore currents. Results for Okains Bay show that local winds tended to blow in offshore and onshore directions, as the bay is located in a valley, so orographic effects channel and shift the wind directions to angles close to offshore and onshore directions inside the bay. Results also indicated that local winds influence the hydrodynamic currents of pocket beaches that are confined by elevated topography, producing semi-cross shore influences since the winds are topographically channelled to blow in predominantly offshore and onshore directions. This research significantly refines our understanding of micro-tidal pocket beach wave and current processes, including quantification of the filtering effects of headlands on their wave environments, revealing the various and variable influences of tides and winds compared to in open coast beaches; and, significantly, highlighting the role of downcoast headland wave reflection effects. With regard to the latter, this research elucidates some key process differences between pocket and embayed beaches and clarifies reasons why the application of embayed beach models that include refraction and diffraction but exclude reflection effects to the study of pocket beaches is inappropriate for studying pocket beaches. This research also provides methodological and topic suggestions for future research on pocket beach environments, including how to use the improved hydrodynamic knowledge of this study in future studies seeking to better understand pocket beach sediment systems, a topic that was beyond the scope of the current research.

The upwelling and cross-shelf transport dynamics along the Pacific Eastern Boundary is explored using a high resolution ocean model for the last 60 years. Three ocean circulations have been modeled. From North to South, we investigate the dynamics of the Gulf of Alaska (GOA), the California Current System (CCS) and the Humboldt Current System (HCS, also known as the Peru-Chile Current System). The statistics of coastal waters transport are computed using a model passive tracer, which is continuously released at the coast. By looking at the passive tracer concentration distribution, we find that the Pacific Decadal Oscillation modulates the coastal variability of the GOA, the North Pacific Gyre Oscillation controls the upwelling of the CCS, while the El-Niño Southern Oscillation affects the upwelling of Peru and Chile mainly through coastally trapped Kelvin waves. Results also emphasize the key role of the mesoscale eddies in the offshore transport of coastal waters masses. The passive tracer experiments, performed in this study in the GOA, CCS, and HCS, therefore could provide a dynamical framework to understand the dynamics of the upwelling/downwelling and offshore transport of nutrient rich coastal water and to interpret how it responds to atmospheric forcing. This also could reinforce our interpretation (and therefore predictions) in the changes in vertical and offshore advection of other important biogeochemical quantities, essential in understanding ecosystem variability.

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