Application for fault location in electrical power distribution systems

Fault location has been studied deeply for transmission lines due to its importance in power systems. Nowadays the problem of fault location on distribution systems is receiving special attention mainly because of the power quality regulations. In this context, this paper presents an application software developed in Matlabtrade that automatically calculates the location of a fault in a distribution power system, starting from voltages and currents measured at the line terminal and the model of the distribution power system data. The application is based on a N-ary tree structure, which is suitable to be used in this application due to the highly branched and the non- homogeneity nature of the distribution systems, and has been developed for single-phase, two-phase, two-phase-to-ground, and three-phase faults. The implemented application is tested by using fault data in a real electrical distribution power system

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

Synchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data.

Increased blood glucose variability during therapeutic hypothermia and neurological recovery after cardiac arrest

INTRODUCTION. Recent studies suggest that increased blood glucose variability (BGV) is associated with ICU mortality1. Hypothermia is known to induce insulin resistance, thus potentially increasing BGV. No studies however have examined the effect of therapeutic hypothermia (TH) on insulin requirements and BGV. OBJECTIVES. To examine the effect of TH on BGV and its relationship to outcome in patients with coma after cardiac arrest (CA). METHODS. We prospectively studied 132 consecutive comatose CA patients treated with TH (target core temp 33_C for 24 h, using surface cooling). All patients were treated with intravenous insulin (blood glucose target 6-8 mM), according to a written algorithm, with nurse-driven adjustment of insulin dose. For each patient, standard deviation of repeated blood glucose samples was used to calculate BGV. Two time-points, comparable in duration, were studied: TH (stable maintenance phase, i.e. 6-24 h, core temp ± 33_C) vs. Normothermia (NT, i.e. after rewarming, stable normothermic phase, core temp ± 37_C). Mortality and neurological recovery (Glasgow-Pittsburgh Cerebral Performance Categories, CPC, dichotomized as good = CPC 1-2 vs. poor = CPC 3-5) were assessed at hospital discharge. Statistical analysis was performed with ANOVA for repeated measures. RESULTS. Compared to NT, TH was associated with increased intravenous insulin dose (0.8 ± 1.1 vs. 1.6 ± 2 U/h, P\0.0001), higher mean (6.9 ± 1.3 vs. 7.7 ± 1.8 mM, P\0.0001) and maximum (9.1 ± 3.7 vs. 10.9 ± 3.6 mM, P\0.0001) blood glucose, and increased BGV (1.3 ± 1.2 vs. 1.7 ± 1.1 mM, P = 0.004). Increased BGV was strongly associated with mortality (2.5 ± 1.5 mM in non-survivors vs. 1.6 ± 1 mM in survivors, P\0.001) and worse outcome (2.3 ± 1.4 mM in patients with poor vs. 1.5 ± 0.8 mM in those with good neurological recovery, P\0.0001). CONCLUSIONS. Therapeutic hypothermia is associated with increased insulin requirements and higher blood glucose variability,which in turn correlateswithworse prognosis in patientswith post- CA coma. Strategies aimed to maintain stable glycemic profile and avoid blood glucose variability might contribute to optimize the management of TH and may translate into better outcome.

Immunoscintigraphy with antigranulocyte monoclonal antibodies for the diagnosis of septic loosening of hip prostheses.

To determine the value of immunoscintigraphy (IS) with antigranulocyte monoclonal antibodies (Mab) in the diagnosis of subacute or chronic infection of hip prostheses, we prospectively studied 57 patients (23 women and 34 men; age 29-92 years, mean 72.7 years) sent to our institution in the past 6 years for clinical suspicion of septic loosening of a hip prosthesis. Nineteen patients had bilateral prostheses and one of them was studied twice. A total of 78 prostheses were examined. All patients had three-phase bone scans followed by IS with technetium-99m antigranulocyte Mab BW 250/183. Intervals between bone scans and IS varied from 2 days to 4 weeks. Final diagnosis was assessed by culture in 48 cases (articular puncture or intraoperative sampling) and by clinical follow-up of at least 8 months in 30 cases. Twelve prostheses were considered septic and 66 non-septic. The overall sensitivity and specificity were 92% and 64% respectively for bone scans, 67% and 75% for IS and 67% and 84% for both modalities together. In three cases, IS was doubtful and the final clinical diagnosis was negative for infection. False-positive results were observed in the presence of massive loosening of the prosthesis or in association with metaplastic peri-articular bone formation. In three of the four false-negative results, infection was proven only after enrichment of the culture, and the bacterium was Staphylococcus epidermidis. In 12/33 (36%) positive bone scans IS allowed the diagnosis of infection to be excluded. Overall accuracy of both modalities together was 81% and the negative predictive value was 93%, which compares favourably with the results reported for other non-invasive methods.

Eficiència energètica aplicada a les instal·lacions de la Universitat de Vic

En termes generals, es pot definir l’Eficiència Energètica com la reducció del consum d’energia mantenint els mateixos serveis energètics, sense disminuir el nostre confort i qualitat de vida, protegint el medi ambient, assegurant el proveïment i fomentant un comportament Sostenible al seu ús. L’objectiu principal d’aquest treball, és reduir el consum d’energia i terme de potència contractat a la Universitat de Vic, aplicant un programa d’estalvi amb mesures correctores en el funcionament de les seves instal·lacions o espais. Per tal de poder arribar a aquest objectiu marcat, prèviament s’ha realitzat un estudi acurat, obtenint tota la informació necessària per poder aplicar les mesures correctores a la bossa més important de consum. Un cop trobada, dur a terme l’estudi de la viabilitat de la inversió de les mesures correctores més eficients, optimitzant els recursos destinats. L’espai on s’ha dut a terme l’estudi, ha estat a l’edifici F del Campus Miramarges, seguint les indicacions d’Arnau Bardolet (Cap de Manteniment de la UVIC). Aquest edifici consta d’un entresol, baixos i quatre plantes. L’equip de mesura que s’ha fet servir per realitzar l’estudi, és de la marca Circutor sèrie AR5-L, aquests equips són programables que mesuren, calculen i emmagatzemen en memòria els principals paràmetres elèctrics en xarxes trifàsiques. Els projectes futurs complementaris que es podrien realitzar a part d’aquest són: instal·lar sensors, instal·lar mòduls convertidors TCP/IP, aprofitar la xarxa intranet i crear un escada amb un sinòptic de control i gestió des d’un punt de treball. Aquest aplicatiu permet visualitzar en una pantalla d’un PC tots els estats dels elements controlats mitjançant un sinòptic (encendre/parar manualment l’enllumenat i endolls de les aules, estat d’enllumenat i endolls de les aules, consums instantanis/acumulats energètics, estat dels passadissos entre altres) i explotar les dades recollides a la base de dades. Cada espai tindria la seva lògica de funcionament automàtic específic. Entre les conclusions més rellevants obtingudes en aquest treball s’observa: · Que és pot reduir la potència contractada a la factura a l’estar per sota de la realment consumida. · Que no hi ha penalitzacions a la factura per consum de reactiva, ja que el compensador funciona correctament. · Que es pot reduir l’horari de l’inici del consum d’energia, ja que no correspon a l’activitat docent. · Els valors de la tensió i freqüència estan dintre de la normalitat. · Els harmònics estan al llindar màxim. Analitzant aquestes conclusions, voldria destacar les mesures correctores més importants que es poden dur a terme: canvi tecnològic a LED, temporitzar automàticament l’encesa i apagada dels fluorescents i equips informàtics de les aules “seguint calendari docent”, instal·lar sensors de moviment amb detecció lumínica als passadissos. Totes les conclusions extretes d’aquest treball, es poden aplicar a tots els edificis de la facultat, prèviament realitzant l’estudi individual de cadascuna, seguint els mateixos criteris per tal d’optimitzar la inversió.

Grain boundaries in vortex matter

We explore the statistical properties of grain boundaries in the vortex polycrystalline phase of type-II superconductors. Treating grain boundaries as arrays of dislocations interacting through linear elasticity, we show that self-interaction of a deformed grain boundary is equivalent to a nonlocal long-range surface tension. This affects the pinning properties of grain boundaries, which are found to be less rough than isolated dislocations. The presence of grain boundaries has an important effect on the transport properties of type-II superconductors as we show by numerical simulations: our results indicate that the critical current is higher for a vortex polycrystal than for a regular vortex lattice. Finally, we discuss the possible role of grain boundaries in vortex lattice melting. Through a phenomenological theory we show that melting can be preceded by an intermediate polycrystalline phase.

Preventing Cracking at Diaphragm/Plate Girder Connections in Steel Bridges, HR-393, 1998

Some of the Iowa Department of Transportation (Iowa DOT) continuous, steel, welded plate girder bridges have developed web cracking in the negative moment regions at the diaphragm connection plates. The cracks are due to out-of-plane bending of the web near the top flange of the girder. The out-of-plane bending occurs in the "web-gap", which is the portion of the girder web between (1) the top of the fillet welds attaching the diaphragm connection plate to the web and (2) the fillet welds attaching the flange to the web. A literature search indicated that four retrofit techniques have been suggested by other researchers to prevent or control this type of cracking. To eliminate the problem in new bridges, AASHTO specifications require a positive attachment between the connection plate and the top (tension) flange. Applying this requirement to existing bridges is expensive and difficult. The Iowa DOT has relied primarily on the hole-drilling technique to prevent crack extension once cracking has occurred; however, the literature indicates that hole-drilling alone may not be entirely effective in preventing crack extension. The objective of this research was to investigate experimentally a method proposed by the Iowa DOT to prevent cracking at the diaphragm/plate girder connection in steel bridges with X-type or K-type diaphragms. The method consists of loosening the bolts at some connections between the diaphragm diagonals and the connection plates. The investigation included selecting and testing five bridges: three with X-type diaphragms and two with K-type diaphragms. During 1996 and 1997, these bridges were instrumented using strain gages and displacement transducers to obtain the response at various locations before and after implementing the method. Bridges were subjected to loaded test trucks traveling in different lanes with speeds varying from crawl speed to 65 mph (104 km/h) to determine the effectiveness of the proposed method. The results of the study show that the effect of out-of-plane loading was confined to widths of approximately 4 in. (100 mm) on either side of the connection plates. Further, they demonstrate that the stresses in gaps with drilled holes were higher than those in gaps without cracks, implying that the drilling hole technique is not sufficient to prevent crack extension. The behavior of the web gaps in X-type diaphragm bridges was greatly enhanced by the proposed method as the stress range and out-of-plane distortion were reduced by at least 42% at the exterior girders. For bridges with K-type diaphragms, a similar trend was obtained. However, the stress range increased in one of the web gaps after implementing the proposed method. Other design aspects (wind, stability of compression flange, and lateral distribution of loads) must be considered when deciding whether to adopt the proposed method. Considering the results of this investigation, the proposed method can be implemented for X-type diaphragm bridges. Further research is recommended for K-type diaphragm bridges.

Planning, Developing, and Implementing the Iowa Pavement Marking Management System (IPMMS): Phases I and II, 2006

With an annual pavement marking program of approximately $2 million and another $750 thousand invested in maintenance of durable markings each year, the Iowa DOT is seeking every opportunity to provide all-year markings staying in acceptable condition under all weather conditions. The goal of this study is to analyze existing pavement marking practices and to develop a prototype Pavement Marking Management System (PMMS). This report documents the first two phases of a three-phase research project. Phase I includes an overview of the Iowa DOT’s existing practices and a literature review regarding pavement marking practices in other states. Based on this information, a work plan was developed for Phases II and III of this study. Phase II organized the key components necessary to develop a prototype PMMS for the Iowa DOT. The two primary components are (1) performance/life cycle curves for pavement marking products, and (2) an application matrix tailored to the pavement marking products and roadway and environmental conditions faced by the Iowa DOT. Both components will continue to be refined and tailored to Iowa materials and conditions as more performance data becomes available.

1003-001 Williamson Pond Final Report

Williamson Pond is a 26-acre publicly owned lake located about 2 miles east of the town of Williamson, in Lucas County. It has a watershed area of 1,499 acres. It has been managed since 1976 by the Lucas County Conservation Board (while still under state ownership) for fishing, boating, hunting, picnicking and other passive uses. Designated uses are Class AI, primary contact, and Class B (LW) aquatic life. Williamson Pond is on the 2004 EPA 303(d) List of Impaired Waters. A Total Maximum Daily Load (TMDL) for turbidity and nutrients at Williamson Pond was prepared by IDNR in 2005 and approved by EPA in 2006. The TMDL set reduction targets for both suspended sediment and phosphorus. The Williamson Pond Watershed Management Plan has provided the local work group and partners with information to develop and implement strategies to improve and protect water quality. These strategies are based on a three phase approach that will ultimately lead the removal of Williamson Pond from the Impaired Waters List. The goals identified in this proposal (Phase I) will reduce sediment and phosphorus delivery by 453 tons and 589 pounds annually. The Lucas County SWCD has and will continue to provide leadership on the Williamson Pond Project and has secured the partnerships necessary to address water quality problems and hired a part-time project coordinator to manage, implement, and oversee all activities pertaining to this proposal.

Sähköverkkotiedonsiirtomenetelmän kehittäminen taajuusmuuttajaohjattuihin sähkökäyttöihin

Sähkömoottorin jatkuva-aikainen kunnonvalvonta vaatii tiedonsiirtoa moottorilta ylemmälle tietojärjestelmätasolle, kuten taajuusmuuttajalle. Uusien kaapeleiden asennus on työlästä ja kallista. Moottorin ja taajuusmuuttajan välillä on kuitenkin aina kaapeli, jota käytetään moottorin tehonsyöttöön. Tätä kaapelia on mahdollista käyttää myös tiedonsiirtokanavana. Tässä diplomityössä käsitellään ja tutkitaan sähköverkkotiedonsiirtomenetelmää, jonka avulla voidaan muodostaa Ethernet-yhteys moottorilta taajuusmuuttajalle tai toisinpäin. Työssä kehitetään simulointimalli tiedonsiirtokanavan taajuusriippuvan vaimennuksen simuloimiseen. Lisäksi kehitetään kytkentärajapinta, joka mahdollistaa tiedonsiirron kolmivaiheisessa taajuusmuuttajan syöttämässä moottorikaapelissa. Työssä suunnitellaan ja toteutetaan tiedonsiirtoa varten pilot-laitteisto, jolla tehdään laboratoriotestit. Laboratoriotesteillä varmistetaan menetelmän soveltuvuus. Laboratoriotestien avulla etsitään myös reunaehdot tiedonsiirron toiminnalle ja tiedonsiirtonopeuteen vaikuttavia tekijöitä taajuusmuuttajakäytössä. Lisäksi tarkastellaan menetelmän aiheuttamaa viivettä, joka on tärkeäsäätösovellusten kannalta. Lopuksi arvioidaan menetelmän soveltuvuus käytännön sovelluksiin.

Development of a simulation tool for torsional vibration of branched power transmission system

In this master's thesis a mechanical model that is driven with variable speed synchronous machine was developed. The developed mechanical model simulates the mechanics of power transmission and its torsional vibrations. The mechanical model was developed for the need of the branched mechanics of a rolling mill and the propulsion system of a tanker. First, the scope of the thesis was to clarify the concepts connected to the mechanical model. The clarified concepts are the variable speed drive, the mechanics of power transmission and the vibrationsin the power transmission. Next, the mechanical model with straight shaft line and twelve moments of inertia that existed in the beginning was developed to be branched considering the case of parallel machines and the case of parallel rolls. Additionally, the model was expanded for the need of moreaccurate simulation to up to thirty moments of inertia. The model was also enhanced to enable three phase short circuit situation of the simulated machine. After that the mechanical model was validated by comparing the results of the developed simulation tool to results of other simulation tools. The compared results are the natural frequencies and mode shapes of torsional vibration, the response of the load torque step and the stress in the mechanical system occurred by the permutation of the magnetic field that is arisen from the three phase short circuit situation. The comparisons were accomplished well and the mechanical model was validated for the compared cases. Further development to be made is to develop the load torque to be time-dependent and to install two frequency converters and two FEM modeled machines to be simulated parallel.

Modeling growth and yield of loblolly pinestands under intensive management

Abstract:The objective of this work was to develop and validate a prognosis system for volume yield and basal area of intensively managed loblolly pine (Pinus taeda) stands, using stand and diameter class models compatible in basal area estimates. The data used in the study were obtained from plantations located in northern Uruguay. For model validation without data loss, a three-phase validation scheme was applied: first, the equations were fitted without the validation database; then, model validation was carried out; and, finally, the database was regrouped to recalibrate the parameter values. After the validation and final parameterization of the models, a simulation of the first commercial thinning was carried out. The developed prognosis system was precise and accurate in estimating basal area production per hectare or per diameter classes. There was compatibility in basal area estimates between diameter class and whole stand models, with a mean difference of -0.01 m2ha-1. The validation scheme applied is logic and consistent, since information on the accuracy and precision of the models is obtained without the loss of any information in the estimation of the models' parameters.

APROS code benchmarking inboiling water reactor accident analyses

Diplomityö käsittelee kiehutusvesilaitosten transienttien ja onnettomuuksien analysointia APROS-ohjelmiston avulla. Työ on tehty Teollisuuden Voima Oy:n (TVO) Olkiluoto 1 ja 2 laitosyksiköiden mallin pohjalta. Raportissa esitetään ohjelmiston käyttämiä yhtälöitäja laskentamalleja yleisellä tasolla. Työssä esitellään laitoksen yleispiirteet turvallisuustoimintoineen ja kuvataan ohjelmaan suureksi osaksi aiemmin luotua laskentamallia. Työssä on luetteloitu voimassa olevatlisensiointianalyysit, joiden joukosta on valittu laskentatapauksia ohjelmiston suorituskyvyn arviointia varten. Lisäksi työhön on valittu laskentatapauksia muilla kuin lisensointiin käytetyillä ohjelmilla lasketuista analyyseistä. Lisäksi on suoritettu vertailulaskuja konservatiivisen ja realistisen mallin erojen esille saamiseksi. Laskentatapauksia ovat mm. ylipainetransientti, jäähdytteen menetysonnettomuus ja oletettavissa oleva käyttöhäiriö, jossa pikasulku ei toimi (ATWS). Diplomityön edetessä laitosmallia on kehitetty edelleen lisäämällä joitakin järjestelmiä ja tarkentamalla joidenkin komponenttien kuvausta. Työssä ilmeni, että APROS soveltuu jäähdytteenmenetysonnettomuuden ja suojarakennuksen yhtäaikaiseen analyysiin. APROS.n vaste nopeisiin transientteihin jäi kuitenkin vertailutasosta. Tämän työn perusteella APROS-mallia kehitys jatkuu edelleen siten, että se soveltuisi entistä paremmin myös nopeiden transienttien ja ATWS-tilanteiden kuvaamiseen. Työssä olevaa lisensointianalyysien kuvausta tullaan käyttämään hyväksi selvitettäessä laitoksen turvallisuuden väliarviossa tarvittavien analyysien määrää ja laatua. Nyt saatuja kokemuksia voidaan hyödyntää myös mahdollisen kolmiulotteisen sydänmallin hankinnassa APROS-ohjelmistoon. Tässä diplomityössä esitettyjä parannuksia voidaan käyttää hyväksi SAFIRtutkimusohjelman hankkeiden suunnittelussa.

Role of trabectedin in the treatment of soft tissue sarcoma.

Interest in marine natural products has allowed the discovery of new drugs and trabectedin (ET-743, Yondelis), derived from the marine tunicate Ecteinascidia turbinata, was approved for clinical use in 2007. It binds to the DNA minor groove leading to interferences with the intracellular transcription pathways and DNA-repair proteins. In vitro antitumor activity was demonstrated against various cancer cell lines and soft tissue sarcoma cell lines. In phase I studies tumor responses were observed also in osteosarcomas and different soft tissue sarcoma subtypes. The most common toxicities were myelosuppression and transient elevation of liver function tests, which could be reduced by dexamethasone premedication. The efficacy of trabectedin was established in three phase II studies where it was administered at 1.5 mg/m2 as a 24 h intravenous infusion repeated every three weeks, in previously treated patients. The objective response rate was 3.7%-8.3% and the tumor control rate (which included complete response, partial response and stable disease) was obtained in half of patients for a median overall survival reaching 12 months. In nonpretreated patients the overall response rate was 17%. Twenty-four percent of patients were without progression at six months. The median overall survival was almost 16 months with 72% surviving at one year. Predictive factors of response are being explored to identify patients who are most likely to respond to trabectedin. Combination with other agents are currently studied with promising results. In summary trabectedin is an active new chemotherapeutic agents that has demonstrated its role in the armamentarium of treatments for patients with sarcomas.

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.