Yhteismuotosuodatus taajuusmuuttajan lähdössä

Tässädiplomityössä selvitettiin taajuusmuuttajan synnyttämien yhteismuotoisten häiriöiden syntyä, ominaisuuksia, kulkureittejä sekä erilaisia tekniikoita toteuttaa yhteismuotosuodatus taajuusmuuttajan lähdössä. Työssä suunniteltiin ja mitoitettiin yhteismuotosuodatin, josta valmistettiin prototyyppi. Suodatinta testattiin laboratoriossa ja mittauksissa käytettiin erilaisia suodattimen kapasitanssin arvoja ja neutraalin pisteen kytkennän variaatioita. Mittauksilla selvitettiin suodattimen kyky suodattaa myös yhteismuotoisten jännitteiden lisäksi eromuotoista jännitettä, akselijännitettä ja vaihevirtaa. Mittaustulosten perusteella voitiin todeta suunnitellun suodattimen parantavan merkittävästi taajuusmuuttajalta moottorille syötettävän sähkön laatua ja loiventavan ennen kaikkea yhteismuotoisen jännitepulssin nousureunaa.

Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

Reaaliaikainen Clarken muunnos

Työssä suunniteltiin ja rakennettiin laite, joka suorittaa reaaliaikaisen Clarken muunnoksen kolmivaiheiselle mittaussignaalille. Kolmivaiheisella mittaussignaalilla tarkoitetaan tässä kolmivaiheisesta järjestelmästä mitattuja vaihevirtoja tai -jännitteitä. Lähtö tuottaa kaksivaiheisen mittaussignaalin, jota voidaan tutkia oskilloskooppia. Käyttämällä oskilloskooppia xy-moodissa näytölle piirtyy virta- tai jänniteympyrä. Laitetta voidaan käyttää esimerkiksi taajuusmuuttajien testauksen apuvälineenä, jolloin parametrien muuttamisen vaikutus laitteen tuottaman sähkön laatuun nähdään välittömästi.

Parallel-Operating Three-Phase Voltage Source Inverters – Circulating CurrentModeling, Analysis and Mitigation

The maximum realizable power throughput of power electronic converters may be limited or constrained by technical or economical considerations. One solution to this problemis to connect several power converter units in parallel. The parallel connection can be used to increase the current carrying capacity of the overall system beyond the ratings of individual power converter units. Thus, it is possible to use several lower-power converter units, produced in large quantities, as building blocks to construct high-power converters in a modular manner. High-power converters realized by using parallel connection are needed for example in multimegawatt wind power generation systems. Parallel connection of power converter units is also required in emerging applications such as photovoltaic and fuel cell power conversion. The parallel operation of power converter units is not, however, problem free. This is because parallel-operating units are subject to overcurrent stresses, which are caused by unequal load current sharing or currents that flow between the units. Commonly, the term ’circulatingcurrent’ is used to describe both the unequal load current sharing and the currents flowing between the units. Circulating currents, again, are caused by component tolerances and asynchronous operation of the parallel units. Parallel-operating units are also subject to stresses caused by unequal thermal stress distribution. Both of these problemscan, nevertheless, be handled with a proper circulating current control. To design an effective circulating current control system, we need information about circulating current dynamics. The dynamics of the circulating currents can be investigated by developing appropriate mathematical models. In this dissertation, circulating current models aredeveloped for two different types of parallel two-level three-phase inverter configurations. Themodels, which are developed for an arbitrary number of parallel units, provide a framework for analyzing circulating current generation mechanisms and developing circulating current control systems. In addition to developing circulating current models, modulation of parallel inverters is considered. It is illustrated that depending on the parallel inverter configuration and the modulation method applied, common-mode circulating currents may be excited as a consequence of the differential-mode circulating current control. To prevent the common-mode circulating currents that are caused by the modulation, a dual modulator method is introduced. The dual modulator basically consists of two independently operating modulators, the outputs of which eventually constitute the switching commands of the inverter. The two independently operating modulators are referred to as primary and secondary modulators. In its intended usage, the same voltage vector is fed to the primary modulators of each parallel unit, and the inputs of the secondary modulators are obtained from the circulating current controllers. To ensure that voltage commands obtained from the circulating current controllers are realizable, it must be guaranteed that the inverter is not driven into saturation by the primary modulator. The inverter saturation can be prevented by limiting the inputs of the primary and secondary modulators. Because of this, also a limitation algorithm is proposed. The operation of both the proposed dual modulator and the limitation algorithm is verified experimentally.

Covariant Phase Observables in Quantum Mechanics

The aim of this thesis is to present a solution to the quantum phase problem of the single-mode optical field. The solution is based on the use of phase shift covariant normalized positive operator measures. These measures describe realistic direct coherent state phase measurements such as the phase measurement schemes based on eight-port homodyne detection or heterodyne detection. The structure of covariant operator measures and, more generally, covariant sesquilinear form measures is analyzed in this work. Four different characterizations for phase shift covariant normalized positive operator measures are presented. The canonical covariant operator measure is definded and its properties are studied. Finally, some other suggested phase theories are introduced to investigate their connections to the covariant sesquilinear form measures.

Feeding levels during the growing phase affect the production of primiparous Finnish Landrace ewes

Selostus: Ruokinnan voimakkuuden vaikutus siitosuuhikaritsan tuotantoon