Inom Bolidens industriella nät förekommer övertonsströmmar med sådan amplitud att de förorsakar en övertonshalt i spänningen av 12%. Inom nätet finns ett stort antal olinjära laster som kan vara orsak till förekomsten av dessa övertonsströmmar, dessutom finns faskompenseringsutrustning ansluten vilket sannolikt orsakar förstärkning av övertoner genom resonans. För att kartlägga utbredningen av övertoner inom Bolidens industriella nät så utförs mätningar vid fyra olika driftfall. Inledningsvis görs omfattande mätningar vid normal drift vilket ger en tydlig överblick av problemet i dagsläget. därefter utförs mätningar på strategiska platser i nätet i samband med att kondensatorbatterierna kopplas bort. Avsikten är då att undersöka om faskompenseringsutrustningen ingår i en resonanskrets som påverkar övertonsströmmarna i nätet. Slutligen genomförs en mätning under tiden som kvarnarna i anrikningsverket tas ur drift för reparation och underhåll samt ett antal mätningar under tiden som dessa står stilla. När resultatet från dessa mätningar sedan vägs samman så kan man se att det sannolikt är så att de fyra kvarnarna vid anrikningsverket, vilka regleras med hjälp av frekvensomriktare, genererar stora övertonsströmmar. En övervägande stor andel av problemens ursprung kan alltså avgränsas till ett litet antal maskiner. Mätningar indikerar dessutom att övertonsströmmarna förstärks genom resonans till följd av de kondensatorbatterier som finns anslutna till nätet. Slutligen visar också resultatet att övertonshalten inom nätet är så stor att störningar fortplantar sig till överliggande nät och vidare till intilliggande nät. Eftersom övertonsströmmar kan förorsaka haverier i roterande maskiner, transformatorer och kondensatorbatterier så undersöks om sådan risk föreligger. Enligt beräkningar så kan transformatorn som utsätts för de största övertonsströmmarna endast belastas till 95,5% av märkeffekt under rådande omständigheter. Denna drivs dock i dagsläget vid en mycket lägre belastning varpå inga risker bedöms föreligga. Kondensatorbatterierna utsätts för stora övertonsströmmar. Mätningarna visar också att dessa ingår i en resonanskrets varpå det finns en risk för överbelastning och haveri. I anrikningsverket finns en 630kW motor ansluten till nätspänning. Denna utsätts för stora övertonsströmmar vilket förorsakar ökade förluster i lindningar och järn men eftersom inte heller denna drivs vid märkeffekt så anses ingen risk för överbelastning föreligga. När det gäller roterande maskiner kan dock slitage till följd av övertonsströmmar förekomma utan att maskinen överbelastas och här kan ytterligare undersökningar vara motiverade. I dagsläget finns planer på att installera nya kondensatorbatterier med övertonsfilter i nätet vilket med stor sannolikhet minskar övertonshalten i enlighet med vad mätningarna visar. Mätningarna visar dock också att mer högfrekventa övertoner i spänningen ökar kraftigt när kondensatorbatterierna kopplas bort vilket kan behöva beaktas vid val av filter. Ett antal alternativa eller kompletterande lösningar till övertonsproblematiken finns i rapporten. / Inside the industrial grid located in Boliden the presence of harmonic current is so high that It causes a total harmonic distortion of 12% in the voltage.  There is a large number of non-linear loads that can cause this distortion connected to the grid, furthermore there is phase compensating equipment connected that may enhance harmonic currents due to resonance. To investigate the cause and the consequences of harmonics in the grid measurements are conducted during four different modes of operation. Initially a large number of measurements are performed during normal operation to show the harmonic distribution. Then measurements at strategic places in the grid are performed while the phase compensating equipment is disconnected with the objective to show if this equipment is part of a resonance circuit. Finally, measurements are performed while the mills in the dressing plant are taken out of production and additional measurements while they are at standstill. The results of all these tests show that there is a high probability that the four mills at the dressing plant, regulated by inverters, causes large harmonic currents. A predominantly large portion of the harmonic current sources has been isolated in a small number of loads. The result also show that these harmonic currents are enhanced by resonance between the phase compensation equipment and inductive elements of the grid. The resulting distortion is of such gravity that it propagates to adjacent grids via the main grid. Since harmonics can cause breakdowns in rotating machinery, transformers and phase compensating equipment, the risk of this is investigated. Calculations show that at current levels the transformers connecting the industrial grid to the main grid can only be operated at 95,5%. The transformer is currently operating at a far lower rate and no risk of damage is at hand. The phase compensation equipment is exposed to large harmonic current. They are also part of a resonance circuit and the assessment is that they are at risk of breakdown. In the dressing plant, there is a 630kW induction motor connected directly to the grid. This motor Is subjected to large harmonic currents causing losses in copper wiring and the iron core but since this machine runs below rated power the assessment is that this does not put it at risk of breakdown. However, there are other ways that a machine of this kind can be damaged due to harmonics and further investigation into this may be warranted. There are plans of installing new, filtered, phase compensating equipment to the grid which most likely will reduce the harmonic content in accordance with the measurements in this report. However, the measurements also show that higher frequency harmonics in the voltage are enhanced when the phase compensation is disconnected, this may have to be taken in to account when the filters are designed. A number of alternative or additional solutions to the harmonic problem is presented in the report.

This thesis presents a comprehensive solution technique for power system harmonic analysis with unbalanced load flow conditions. It is based on multiphase modelling of the system in phase quantities. Two of the most important features of this technique are the multiphase approach to the harmonic load flow problem, and the capability to add component nonlinearities easily. The first feature allows the technique to be used for either single-phase or three-phase, and for either balanced or unbalanced harmonic analysis. The second feature allows the later addition of power electronic device models. The technique is simple in concept. The nonlinear elements are first modelled as harmonic Norton equivalent circuits based on the network load flow conditions. These linear circuits are then included in the network solution with multiphase load flow constraints and network unbalances. Once the new load flow solutions are obtained, improved Norton equivalent circuits can be calculated, which in turn are used for improved network solutions. The entire solution scheme is therefore iterative, and stops when certain convergence criteria are met. The unbalanced harmonics from nonlinear inductors, synchronous machines and static compensators with thyristor-controlled reactors are studied in this thesis. The convergence properties of the technique are investigated with test cases and theoretical analysis. In addition to the harmonic load flow analysis, this technique can also be used as an improved initialization procedure for the Electromagnetic Transient Program (EMTP). / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Student Number : 9811492X - MSc dissertation - School of Electrical and Information Engineering - Faculty of Engineering and the Built Environment / This dissertation discusses the development of an ATP model of a network to aid measurement techniques in a harmonic evaluation. A theoretical back- ground discussion of various pieces of equipment and their signi#12;cance to har- monics is included. National Electricity Regulator (NRS 048) standards are discussed with refer- ence to performing a basic investigation and short comings. A test study was performed on the Brandspruit Mine in Secunda. ATP models are developed for equipment relevant to the test case, these in- clude AC{AC converters, AC{DC converters, three phase transformers and cables. Finally the measured test case is compared to simulation results and conclusions drawn.

Doctor of Philosophy / Department of Physics / Brett DePaola / Zenghu Chang / Extremely broad bandwidth attosecond pulses (which can support 16as pulses) have been demonstrated in our lab based on spectral measurements, however, compensation of intrinsic chirp and their characterization has been a major bottleneck. In this work, we developed an attosecond streak camera using a multi-layer Mo/Si mirror (bandwidth can support ~100as pulses) and position sensitive time-of-flight detector, and the shortest measured pulse was 107.5as using DOG, which is close to the mirror bandwidth. We also developed a PCGPA based FROG-CRAB algorithm to characterize such short pulses, however, it uses the central momentum approximation and cannot be used for ultra-broad bandwidth pulses. To facilitate the characterization of such pulses, we developed PROOF using Fourier filtering and an evolutionary algorithm. We have demonstrated the characterization of pulses with a bandwidth corresponding to ~20as using synthetic data. We also for the first time demonstrated single attosecond pulses (SAP) generated using GDOG with a narrow gate width from a multi-cycle driving laser without CE-phase lock, which opens the possibility of scaling attosecond photon flux by extending the technique to peta-watt class lasers. Further, we generated intense attosecond pulse trains (APT) from laser ablated carbon plasmas and demonstrated ~9.5 times more intense pulses as compared to those from argon gas and for the first time demonstrated a broad continuum from a carbon plasma using DOG. Additionally, we demonstrated ~100 times enhancement in APT from gases by switching to 400 nm (blue) driving pulses instead of 800 nm (red) pulses. We measured the ellipticity dependence of high harmonics from blue pulses in argon, neon and helium, and developed a simple theoretical model to numerically calculate the ellipticity dependence with good agreement with experiments. Based on the ellipticity dependence, we proposed a new scheme of blue GDOG which we predict can be employed to extract intense SAP from an APT driven by blue laser pulses. We also demonstrated compression of long blue pulses into >240 µJ broad-bandwidth pulses using neon filled hollow core fiber, which is the highest reported pulse energy of short blue pulses. However, compression of phase using chirp mirrors is still a technical challenge.

M.Ing. / The increased used of non-linear loads within the power system during recent years have resulted in deviations from the perfect sinusoidal voltage and current waveform. This deviation from the perfect sinusoidal waveform can be expressed according to Fourier analysis by a set of co-sinusoidal waveforms having frequencies, which are a multiple of the fundamental frequency, referred to as harmonics. Non-linear loads are generally characterised by harmonic currents. It is therefore often preferred to express the harmonic emission limits in terms of harmonic currents rather than harmonic voltages. In order to translate the harmonic currents into harmonic voltages the harmonic impedance of the power system must be known. The power system's harmonic impedance can be assessed via computational, simulation and measurement techniques. The study will concentrate on the estimation of the harmonic impedance of a 33kV power system by implementing two online frequency domain measurement techniques. Both techniques are applied at the point of delivery of a dominant nonlinear load during normal and energisation load conditions with its power factor correction capacitor bank in and out off service. The estimated harmonic impedance is then compared with the calculated and simulated harmonic impedance.

ABSTRACT Power transformers are key components for electrical energy transfer in a power system. Stability and security of transformer protection are important to system operation. Many maloperation cases of transformer differential protection are caused by inrush current problems. The phenomenon of transformer inrush current has been widely discussed in literature. Therefore, this research only discussed and analyzed inrush current problems to transformer differential protection. To understand the inrush current problems on differential protection, transformer simulation models were presented using Matlab/Simulink. Differential relay simulations for internal and external faults, and relay performance during current transformer saturation were performed using PSCAD. Recommendations were made on methods of reducing the blocking time of differential protection during inrush conditions.

It is well known that the n-th eigenfunction to one-dimensional Sturm-Liouville eigenvalue problems has exactly n-1 nodes, i.e. non-degenerate zeros. For higher dimensions, it is much more complicated to obtain general statements on the zeros of eigenfunctions. The author states a new conjecture on the number of nodal domains of spherical harmonics, i.e. of connected components of S^2 \ N(u) with the nodal set N(u) = (x in S^2 : u(x) = 0) of the eigenfunction u, and proves it for the first six eigenvalues. It is a sharp upper bound, thus improving known bounds as the Courant nodal domain theorem, see S. Y. Cheng, Comment. Math. Helv. 51, 43-55 (1976; Zbl 334.35022). The proof uses facts on real projective plane algebraic curves (see D. A. Gudkov, Usp. Mat. Nauk 29(4), 3-79, Russian Math. Surveys 29(4), 1-79 (1979; Zbl 316.14018)), because they are the zero sets of homogeneous polynomials, and the spherical harmonics are the restrictions of spherical harmonic homogeneous polynomials in the space to the plane. / Series: Preprint Series / Department of Applied Statistics and Data Processing

<p>Image rendering is the process of creating realistic computer images from  geometric models and physical laws of light and reflection. This master thesis deals mainly with the numerical intricacies of implementing an image renderer using spherical harmonics. It investigates how to calculate the reflection of light in a surface using the Phong model, and employs ray tracing to create a realistic image of a geometric model. Further, it investigates different ways of calculating the spherical harmonic representation of a function defined on the sphere. The thesis also deals with the implementation of self-shadowing, and the effects of adding this component to the rendering equation.</p>