Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Prospects of up-rating existing high voltage direct current (HVDC) transmission schemes, as well as the conversion of existing alternating current (AC) to direct current (DC) lines and the development of new HVDC schemes in sub-Saharan Africa, have led to renewed interest in DC research. The radio interference (RI), audible noise (AN) and corona loss (CL) performance of HVDC transmission lines are critical factors when assessing the reliability of the line design. The RI performance is especially important when considering the successful transmission of the carrier signal of the power line carrier (PLC) system. The PLC system is the main form of communication between teleprotection devices on the Cahora Bassa HVDC scheme. The aim of the dissertation is to devise modelling as well as metrological techniques to characterise DC conductor corona. A particle-in-cell (PIC) computational code is developed to gain a better understanding of the physical processes that occur during corona events. The numerical code makes use of the charge simulation method (CSM) and nite element method (FEM) to solve for the Laplace and Poisson eld equations. Higher-order basis functions are implemented to obtain a more accurate solution to the Poisson equation. The computational tool yields insight into the mathematical models for the various ionization, attachment and electron avalanche processes that give rise to corona currents. Together with a designed and developed electrometer-type circuit, the numerical code assists the visualisation of the space charge particle dynamics that form in the electrode gap during corona events. The metrological techniques consider the wideband time domain (TD) as well as the frequency domain (FD) information of the measured corona pulses in the presence of noise. These are then compared to the narrowband CISPR standard measurements centred around 500kHz. The importance of impedance matching when attempting to derive a wideband excitation function is investigated. The TD measurements are quite distinct from the well-published FD measurements, and consider the pulse shape, pulse spectrum and pulse repetition rates. The use of three possible conductor corona test methods to study direct current conductor RI performance under both positive and negative polarities is investigated at high altitude in this dissertation. These include a small corona cage, a short test line and the Eskom Megawatt Park large outdoor corona cage. Derived wideband and narrowband monopolar DC RI excitation functions at 500kHz are consolidated with existing radio noise (RN) measurement protocols and prediction methods. The use of a corona cage to derive excitation functions for monopolar RI predictions is explored and it is shown that a small corona cage, due to the build-up of space charge in the small distance between the electrodes, cannot be used to predict the RI levels on HVDC transmission lines accurately. As a consequence of the physics, computational modelling and both frequency and time domain measurements, it is now possible to explain why a small cage system prevents the accurate RI prediction on transmission lines. The large outdoor corona cage and short test line RI performance predictions agree with existing empirical prediction formulas. / AFRIKAANSE OPSOMMING: Vooruitsigte van die opgradering van bestaande hoogspanningsgelykstroom transmissielyn skemas, asook die omkering van bestaande wisselstroom na gelykstroom lyne en die ontwikkeling van nuwe hoogspanningsgelykstroom skemas in sub-Sahara Afrika, het gelei to hernude belangstelling in gelykstroomnavorsing. Die korona-werkverrigting van hoogspanningsgelykstroom oorshoofselyne in terme van radiosteuring, hoorbare-geraas en koronaverliese is kritiese faktore om in aanmerking te neem wanneer die betroubaarheid van die lynontwerp geëvalueer word. Die radiosteuring-werkverrigting is veral van belang tot die suksesvolle oordrag van die kraglyndragolf draersein wat die hoof kommunikasievorm tussen beskermingstoerusting op die Cahora Bassa transmissielyn skema is. Die doel van hierdie proefskrif is om modellering- sowel as meettegnieke te ontwerp om gelykstroomgeleierkorona te karakteriseer. 'n Partikel-in-sel numeriese kode is ontwikkel om 'n beter begrip te verkry van die siese prosesse gedurende koronagebeure. Die numeriese kode maak gebruik van die lading-simulasiemetode, sowel as die eindige element metode om die Laplace en Poisson veldvergelykings op te los. Hoër-orde basisfunksies is geimplimenteer om 'n meer akkurate oplossing vir die Poisson vergelyking te verkry. Die numeriese kode bied insig tot die wiskundige modelle vir die verskeie ionisasie-, aanhegtings- en lawineprosesse wat lei tot koronastrome in die area om die hoogspanningsgeleier. Die numeriese kode, saam met 'n elektro-meter wat ontwerp en ontwikkel is, dra by tot die begrip van die ruimtelading partikeldinamika wat onstaan in die elektrodegaping gedurende koronagebeure. Die meettegnieke neem die wyeband tydgebied- en frekwensiegebiedinformasie van die koronapulse in ag in die teenwoordigheid van geraas. Dit word dan vergelyk met die nouband CISPR meetstandaard vir 'n frekwensie van 500kHz. Die belangrikheid van impedansie-aanpassing vir wyeband metings met die doel om opwekkingsfunksies af te lei, word ondersoek. Die tydgebiedmetings verskil van die algemene frekwensiegebiedmetings, en ondersoek die pulsvorm, -spektrum en -herhalingskoers. Die gebruik van drie moontlike koronageleier-toetsmetodes om gelykstroom radiosteurings-werkverrigting vir positiewe en negatiewe polariteite te bestudeer by hoë vlakke bo seespieël word ondersoek in die proefskrif. Dit sluit in 'n klein koronakou, 'n kort toetslyn en die Eskom Megawatt Park groot buitelug-koronakou. Afgeleide wye- en nouband monopolêre gelykstroom radiosteuring opwekkingsfunksies by 500kHz word gekonsolideer met bestaande radioruis metingsprotokolle en voorspellingsmetodes. Die gebruik van 'n koronakou om opwekkingsfunksies af te lei vir monopolêre radiosteuringvoorspellings is ondersoek en daar is gevind dat 'n klein koronakou nie gebruik kan word om radiosteuringvlakke op hoogspanningsgelykstroom transmissielyne akkuraat te voorspel nie. Dit is as gevolg van die opbou van ruimtelading in die klein elektrodegaping. Met behulp van die sika, numeriese modellering en beide die frekwensie- en tydgebiedmetings, is dit nou moontlik om te verklaar waarom die klein koronakou die akkurate radiosteuringvoorspellings op transmissielyne onmoontlik maak. Die groot buitelug-koronakou en kort toetslyn radiosteuringvoorspellings stem ooreen met bestaande empiriese voorspellings formules.

Cette thèse a été consacrée à l'étude des réseaux multi-terminaux haute tension à courant continu (MTDC). Les principales contributions étaient dans le domaine du contrôle automatique non linéaire, appliquées aux systèmes électriques, électronique de puissance et les sources d'énergie renouvelables. Le travail de recherche a été lancé avec l'intention de combler certaines lacunes entre la théorie et la pratique, en particulier: 1) d'enquêter sur diverses approches de contrôle pour le but d'améliorer la performance des systèmes MTDC; 2) d'établir des connexions entre la conception du contrôle empiriques existantes et analyse théorique; 3) d'améliorer la compréhension du comportement multi-échelle de temps des systèmes MTDC caractérisés par la présence de transitoires lents et rapides en réponse aux perturbations externes. En conséquence, ce travail de thèse peut être mis en trois domaines, à savoir la conception non linéaire de commande de systèmes MTDC, analyse des comportements dynamiques de système MTDC et l'application de systèmes MTDC pour le contrôle de fréquence des systèmes de climatisation. / This dissertation was devoted to the study of multi-terminal high voltage direct current (MTDC) networks. The main contributions were in the field of nonlinear automatic control, applied to power systems, power electronics and renewable energy sources. The research work was started with the intention of filling some gaps between the theory and the practice, in particular: 1) to investigate various control approaches for the purpose of improving the performance of MTDC systems; 2) to establish connections between existing empirical control design and theoretical analysis; 3) to improve the understanding of the multi-time-scale behavior of MTDC systems characterized by the presence of slow and fast transients in response to external disturbances. As a consequence, this thesis work can be put into three areas, namely nonlinear control design of MTDC systems, analysis of MTDC system's dynamic behaviors and application of MTDC systems for frequency control of AC systems.

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.

En permettant la transmission de fortes puissances sur de grandes distances, les réseaux en haute tension à courant continu (HTCC) représentent l'avenir du transport de l'énergie électrique. Des équipements tels que les postes sous enveloppe métallique (PSEM) seront indispensables dans ces réseaux pour répartir le flux d'énergie, interrompre ou isoler certaines branches. Leur conception nécessite la prise en compte, pour les parties isolantes, de phénomènes spécifiques liés à l’application de champs électriques continus, comme la dépendance de la résistivité avec le champ et la température, mais également l’accumulation de la charge d'espace qui contribue à augmenter sensiblement les risques de claquage. Dans le composite étudié (résine époxyde chargée d’alumine), ce phénomène commence à se manifester dès que les valeurs de champ excèdent quelques kV/mm, correspondant à l’ordre de grandeur des contraintes envisagées dans les futurs PSEM HTCC.Bien que des techniques existent pour déterminer la répartition de ces charges dans les isolants solides, aucune n’est à ce jour directement applicable aux structures isolantes installées dans les PSEM HTCC.L’objectif de ce travail est ainsi de concevoir et de mettre en place une technique de mesure des charges d’espace et du champ électrique interne qui soit à résolution spatiale, non destructive et adaptée à une géométrie d’isolateur cylindrique, de type support isolant de jeu de barres.En utilisant le dispositif expérimental mis en place, le comportement du composite vis-à-vis de la charge d’espace est par la suite étudié, notamment en fonction de différentes contraintes électrothermiques représentatives du fonctionnement des PSEM. Le but final est d'aider à l'optimisation de la conception de ce type d’isolateur, en se basant sur l’analyse des résultats issus de mesures de charges d’espace. / The trend today is to develop high voltage direct current (HVDC) technology for the future electric network because it offers some advantages for the transmission on long distances. The development of HVDC networks leads to an increasing need of gas insulated substations (GIS). A problem to be dealt with when an insulator is subjected to a continuous electric field is the variation of the resistivity with the electric field and the temperature and the accumulation of space charges that can lead to dielectric breakdown. In alumina-filled epoxy resin, used as insulating material for GIS spacer, the influence of space charge start to come out when the electric fields exceed several kV/mm, corresponding to values envisaged for the future HVDC GIS.Despite that non-destructive methods exist to determine the space charge distribution in solid insulators, none of them are directly applicable to insulation structures installed in the HVDC GIS.So, the main objective of this work is to design and set up a measurement technique to observe the internal electric field and the accumulated charges. The developed method must be non-destructive and adapted for a cylindrical geometry of an insulator used as a busbar insulation support.By using the experimental bench set up, the behavior of the composite material regarding the space charge will be studied, in particular according to different thermoelectric stresses. The final aim is to contribute to the optimization of the design of this type of insulator, based on the results from space charge measurements.

Les travaux de cette thèse portent sur l'intégration dans le réseau électrique du limiteur supraconducteur de courant (SCFCL). Un modèle du ruban supraconducteur ont été développé et validé grâce à une comparaison avec des tests expérimentaux. Premièrement, ce modèle a permis le dimensionnement du SCFCL du projet Eoccoflow (projet européen). Dans un deuxième temps, le modèle de SCFCL est intégré dans différents types de réseau. D'une part, l'intégration du SCFCL dans les réseaux haute tension continu maillés rend vraisemblable la protection de tels réseaux. D'autre part, grâce au SCFCL de nouvelles architectures du réseau de distribution sont proposées permettant l'intégration massive de génération distribuée. Cette thèse se clot sur le dimensionnement et les tests d'un SCFCL pour un réseau à taille réduite. / This PhD deals with superconducting fault current limiter (SCFCL) network integration. A model of a superconducting tape had been developed and validated in comparison with experimental quench tests. This SCFCL model allowed us to design the SCFCL of the european project Eccoflow. Using this SCFCL model, SCFCLs are integrated in various types of networks. On one hand, SCFCL benefits are first studied in case of meshed HVDC networks. Indeed, the SCFCL makes realistic the protection of such networks. On the other hand, thanks to the SCFCL some new distribution network topologies are suggested in order to increase the distributed generation integration capacity. This PhD ends with the design and the test of a SCFCL in a downsize scale network.

Thesis submitted in fulfillment of the requirements for the degree Master of Technology: Electrical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology 2013 / The development of power electronics did remove most of technical limitations that high voltage direct current (HVDC) used to have. HVDC, now, is mostly used for the transmission of bulk power over long distances and for the interconnection of asynchronous grid. Along with the development of the HVDC, the growth of power demand also increased beyond the utilities capacities. Besides the on-going increasing of power demand, the reforms in electricity market have led to the liberalization and the incorporation of Independent power providers in power system operation. Regulations and rules have been established by regulating authority for grid integration of Independent power providers. With the expected increase of penetration level of those new independent power providers, result of economic reason and actual green energy trend, best method of integration of those new power plants are required. In this research HVDC technology, namely VSC-HVDC is used as interface for connecting independent power providers units to the grid. VSC-HVDC has various advantages such as short-circuit contribution and independent control of active and reactive power. VSC-HVDC advantages are used for a safe integration of IPPs and make them participate to grid stabilization. MATLAB/Simulink simulations of different grid connected, through VSC-HVDC system, IPPs technologies models are performed. For each IPP technology model, system model performances are studied and dynamics responses during the disturbance are analyzed in MATLAB/ Simulink program. The simulation results show that the model satisfy the standard imposed by the regulating authority in terms of power quality and grid support. Also the results show the effect of the VSC-HVDC in preventing faults propagation from grid to integrated IPPs units.

Modern interconnected power systems are becoming highly complex and sophisticated, while increasing energy penetrations through congested inter-tie lines causing the operating point approaching stability margins. This as a result, exposes the overall system to potential low frequency power oscillation phenomena following disturbances. This in turn can lead to cascading events and blackouts. Recent approaches to counteract this phenomenon are based on utilization of wide area monitoring systems (WAMS) and power electronics based devices, such as flexible AC transmission systems (FACTS) and HVDC links for advanced power oscillation damping provision. The rise of hybrid AC-DC power systems is therefore sought as a viable solution in overcoming this challenge and securing wide-area stability. If multiple FACTS devices and HVDC links are integrated in a scheme with no supervising control actions considered amongst them, the overall system response might not be optimal. Each device might attempt to individually damp power oscillations ignoring the control status of the rest. This introduces an increasing chance of destabilizing interactions taking place between them, leading to under-utilized performance, increased costs and system wide-area stability deterioration. This research investigates the development of a novel supervisory control scheme that optimally coordinates a parallel operation of multiple FACTS devices and an HVDC link distributed across a power system. The control system is based on Linear Quadratic Gaussian (LQG) modern optimal control theory. The proposed new control scheme provides coordinating control signals to WAMS based FACTS devices and HVDC link, to optimally and coherently counteract inter-area modes of low frequency power oscillations inherent in the system. The thesis makes a thorough review of the existing and well-established improved stability practises a power system benefits from through the implementation of a single FACTS device or HVDC link, and compares the case –and hence raises the issue–when all active components are integrated simultaneously and uncoordinatedly. System identification approaches are also in the core of this research, serving as means of reaching a linear state space model representative of the non-linear power system, which is a pre-requisite for LQG control design methodology.

No description available.

Transmission pricing and congestion management are two important aspects of modern power sectors working under a deregulated environment or moving towards a deregulated system (open access) from a regulated environment. The transformation of power sector for open access environment with the participation of private sector and potential power suppliers under the regime of trading electricity as a commodity is aimed at overcoming some of the limitations faced by the vertically integrated system. It is believed that this transformation will bring in new technologies, efficient and alternative sources of power which are greener, self sustainable and competitive. There is ever increasing demand for electrical power due to the changing life style of human beings fueled by modernization and growth. Augmentation of existing capacity, siting of new power plants, and a search for alternate viable sources of energy that have lesser impact on environment are being taken up. With the integration of power plants into the grid depending upon the type, loca- tion and technology used, the cost of energy production also differs. In interconnected networks, power can flow from one point to other point in infinite number of possible paths which is decided by the circuit parameters, operating conditions, topology of network and the connected loads. The transmission facility provided for power transfer has to recover the charges from the entities present in the network based on the extent of utilization. Since power transmission losses account for nearly 4 to 8% of the total generation, this has to be accounted for and shared properly among the entities depending upon the connected generation/load. In this context, this thesis aims to evaluate the shortcomings of existing tracing methods and proposes a tracing method based upon the actual operating conditions of the network taking into account the network parameters, voltage gradient among the connected buses and topology of the network as obtained by the online state estimator/load flow studies. The concept proposed is relatively simple and easy to implement in a given transactional period. The proposed method is compared against one of the existing tracing technique available in literature. Both active and reactive power tracing is handled at one go. The summation of partial contributions from all the sources in any given line of the system always matches with that of the respective base case ow. The AC power flow equations themselves are nonlinear in nature. Since the sum of respective partial flows in a given branch is always equal to the original ow, these are termed as virtual flows and the effect of nonlinearity is still unknown. The virtual flows in a given line are complex in nature and their complex sum is equal to the original complex power flows as in the base case. It is required to determine whether these are the true partial flows. To answer this, a DC equivalent of the original AC network is proposed and is called as the R - P equivalent model. This model consists of only the resistances as that of original network (the resistances of transformers and lines neglecting the series reactance and the shunt charging) only. The real power injections in a AC network i.e. sources into respective buses and loads (negative real power injections) are taken as injection measurements of this R P model and the bus voltages (purely real quantities) are estimated using the method of least squares. Complex quantities are absent in this model and only real terms which are either sums or differences are present. For this model, virtual flows are evaluated and it has been verified that the virtual real power contributions from sources are in near agreement with the original AC network. This implies that the virtual flows determined for the original network can be applied for day-to-day applications. An important feature of the virtual flows is that it is possible to identify counter ow components. Counter flow components are the transactions taking place in opposite direction to the net flow in that branch. If a particular source is produces counter flow in a given line, then it is in effect reducing congestion to that extent. This information is lacking in most of the existing techniques. Counter flows are useful in managing congestion. HVDC links are integrated with HVAC systems in order to transfer bulk power and for the additional advantages they offer. The incremental cost of a DC link is zero due to the closed loop control techniques implemented to maintain constant power transfer (excluding constant voltage or constant current control). Consequently, cost allocation to HVDC is still a problem. The proposed virtual power flow tracing method is extended to HVAC systems integrated with HVDC in order to determine the extent of utilization of a given link by the sources. Before evaluating the virtual contributions to the HVDC links, the steady state operating condition of the combined system is obtained by per-forming a sequential load flow. Congestion is one of the main aspects of a deregulated system, and is a result of several transactions taking place simultaneously through a given transmission facility. If congestion is managed by providing pricing signals for the transmission usage by the parties involved. It can also be due to the non-availability of transmission paths due to line outages as a result of contingencies. In such a case, generation active power redispatch is considered as a viable option in addition to other available controls such as phase shifters and UPFCs to streamline the transactions within the available corridors. The virtual power flow tracing technique proposed in the thesis is used as a guiding factor for managing congestions occurring due to transactions/contingencies to the possible extent. The utilization of a given line by the sources present in the network in terms of real power flow is thus obtained. These line utilization factors are called as T-coefficients and these are approximately constant for moderate increments in active power change from the sources. A simple fuzzy logic based decision system is proposed in order to obtain active power rescheduling from the sources for managing network congestions. In order to enhance the system stability after rescheduling, reactive power optimization has life systems to illustrate the proposed approaches. For secure operation of the network, the ideal proportion of active power schedule from the sources present in the network for a given load pattern is found from network [FLG] matrix. The elements of this matrix are used in the computation of static voltage stability index (L-index). This [FLG] matrix is obtained from the partitioned network YBUS matrix and gives the Relative Electrical Distance (RED) of each of the loads with respect to the sources present in the network. From this RED, the ideal proportion of real power to be drawn by a given load from different sources can be determined. This proportion of active power scheduling from sources is termed as Desired Proportion of Generation (DPG). If the generations are scheduled accordingly, the network operates with less angular separation among system buses (improved angular stability), improved voltage profiles and better voltage stability. Further, the partitioned K[GL] matrix reveals information about the relative proportion in which the loads should draw active power from the sources as per DPG which is irrespective of the present scheduling. Other partitioned [Y ′ GG] matrix is useful in finding the deviation of the present active power output from the sources with respect to the ideal schedule. Many regional power systems are interconnected to form large integrated grids for both technical and economic benefits. In such situations, Generation Expansion Planning (GEP) has to be undertaken along with augmentation of existing transmission facilities. Generation expansion at certain locations need new transmission networks which involves serious problems such as getting right-of-way and environmental clearance. An approach to find suitable generation expansion locations in different zones with least requirements of transmission network expansion has been attempted using the concept of RED. For the anticipated load growth, the capacity and siting generation facilities are identified on zonal basis. Using sample systems and real life systems, the validity of the proposed approach is demonstrated using performance criteria such as voltage stability, effect on line MVA loadings and real power losses.

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